General system of ( A,η) -maximal relaxed monotone variational inclusion problems based on generalized hybrid algorithms

In this paper, a new system of nonlinear (set-valued) variational inclusions involving ( A,η) -maximal relaxed monotone and relative ( A,η) -maximal monotone mappings in Hilbert spaces is introduced and its approximation solvability is examined. The notion of ( A,η) -maximal relaxed monotonicity gen...

Full description

Saved in:
Bibliographic Details
Published inCommunications in nonlinear science & numerical simulation Vol. 15; no. 2; pp. 238 - 251
Main Authors Agarwal, Ravi P., Verma, Ram U.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2010
Subjects
Online AccessGet full text
ISSN1007-5704
1878-7274
DOI10.1016/j.cnsns.2009.03.037

Cover

Abstract In this paper, a new system of nonlinear (set-valued) variational inclusions involving ( A,η) -maximal relaxed monotone and relative ( A,η) -maximal monotone mappings in Hilbert spaces is introduced and its approximation solvability is examined. The notion of ( A,η) -maximal relaxed monotonicity generalizes the notion of general η-maximal monotonicity, including ( H,η) -maximal monotonicity (also referred to as ( H,η) -monotonicity in literature). Using the general ( A,η) -resolvent operator method, approximation solvability of this system based on a generalized hybrid iterative algorithm is investigated. Furthermore, for the nonlinear variational inclusion system on hand, corresponding nonlinear Yosida regularization inclusion system and nonlinear Yosida approximations are introduced, and as a result, it turns out that the solution set for the nonlinear variational inclusion system coincides with that of the corresponding Yosida regularization inclusion system. Approximation solvability of the Yosida regularization inclusion system is based on an existence theorem and related Yosida approximations. The obtained results are general in nature.
AbstractList In this paper, a new system of nonlinear (set-valued) variational inclusions involving ( A,η) -maximal relaxed monotone and relative ( A,η) -maximal monotone mappings in Hilbert spaces is introduced and its approximation solvability is examined. The notion of ( A,η) -maximal relaxed monotonicity generalizes the notion of general η-maximal monotonicity, including ( H,η) -maximal monotonicity (also referred to as ( H,η) -monotonicity in literature). Using the general ( A,η) -resolvent operator method, approximation solvability of this system based on a generalized hybrid iterative algorithm is investigated. Furthermore, for the nonlinear variational inclusion system on hand, corresponding nonlinear Yosida regularization inclusion system and nonlinear Yosida approximations are introduced, and as a result, it turns out that the solution set for the nonlinear variational inclusion system coincides with that of the corresponding Yosida regularization inclusion system. Approximation solvability of the Yosida regularization inclusion system is based on an existence theorem and related Yosida approximations. The obtained results are general in nature.
In this paper, a new system of nonlinear (set-valued) variational inclusions involving (A,[eta])-maximal relaxed monotone and relative (A,[eta])-maximal monotone mappings in Hilbert spaces is introduced and its approximation solvability is examined. The notion of (A,[eta])- maximal relaxed monotonicity generalizes the notion of general [eta]-maximal monotonicity, including (H,[eta])-maximal monotonicity (also referred to as (H,[eta])-monotonicity in literature). Using the general (A,[eta])-resolvent operator method, approximation solvability of this system based on a generalized hybrid iterative algorithm is investigated. Furthermore, for the nonlinear variational inclusion system on hand, corresponding nonlinear Yosida regularization inclusion system and nonlinear Yosida approximations are introduced, and as a result, it turns out that the solution set for the nonlinear variational inclusion system coincides with that of the corresponding Yosida regularization inclusion system. Approximation solvability of the Yosida regularization inclusion system is based on an existence theorem and related Yosida approximations. The obtained results are general in nature. msc: 49J40; 47H10; 65B05
Author Verma, Ram U.
Agarwal, Ravi P.
Author_xml – sequence: 1
  givenname: Ravi P.
  surname: Agarwal
  fullname: Agarwal, Ravi P.
  email: Agarwal@fit.edu
  organization: Department of Mathematical Sciences, Florida Institute of Technology, 150 University Bld, Melbourne, FL 32901, USA
– sequence: 2
  givenname: Ram U.
  surname: Verma
  fullname: Verma, Ram U.
  email: webmaster@internationalpubls.com
  organization: International Publications (USA), 12085 Lake Cypress Circle, Suite I 109, Orlando, FL 32828, USA
BookMark eNqFUM1KJDEQDuKCP-sTeOmTKGzPpjuJmT7sQcQ_ELzsnkM6qdYM6URTGXEEYa8-kW_hQ_gkm3E8eVihoCpV3_el6tsi6yEGIGS3oZOGNoc_ZxMTMOCkpbSbUFZCrpHNZiqntWwlXy81pbIWkvINsoU4o4XVCb5Jns4gQNK-wgVmGKs4VPtvf5-Pfry-HJRcj_rBjWWcwOsHsNUYQ8zl8-peJ6ezi6EMXTB-jqWublPsPYxY9RoLunSuV_rusTxvFn1yttL-OiaXb0b8Tr4N2iPsfORt8uf05PfxeX15dXZxfHRZG8Z4rqXsRMuZ7qd2qhuqGbNGMMu5lFZKaAUHbRrJQLOuEcCttZwJLoeB9oMQkm2TvZVu2e9uDpjV6NCA9zpAnKNiXIq2pbwA2QpoUkRMMKjbVO5PC9VQtbRazdS71WpptaKsxFK--8QyLr-bk5N2_gvurxUXyv33DpJC4yAYsC6BycpG91_-P1XEor4
CitedBy_id crossref_primary_10_1155_2010_472760
crossref_primary_10_1186_1687_1812_2014_161
crossref_primary_10_1007_s13370_013_0171_5
crossref_primary_10_1016_j_cnsns_2011_09_005
crossref_primary_10_1016_j_cnsns_2011_01_024
crossref_primary_10_1080_00036811_2010_538687
crossref_primary_10_4236_ijmnta_2012_13009
crossref_primary_10_1186_1029_242X_2014_407
crossref_primary_10_1080_00036811_2020_1781822
crossref_primary_10_1155_2012_590676
crossref_primary_10_1007_s40096_017_0221_5
crossref_primary_10_1016_j_cnsns_2012_08_026
crossref_primary_10_1186_1029_242X_2014_362
crossref_primary_10_3390_math12131977
crossref_primary_10_1080_01630563_2023_2209147
crossref_primary_10_1155_2014_698593
crossref_primary_10_1016_j_na_2010_08_049
Cites_doi 10.1155/S1048953304403013
10.1016/j.aml.2008.05.001
10.1016/j.camwa.2004.04.037
10.1137/S1052623494250415
10.1006/jmaa.1997.5368
10.5486/PMD.2003.2629
10.2140/pjm.1969.30.475
10.1007/s10957-006-9079-7
10.1016/S0377-0427(99)00250-2
10.4134/JKMS.2004.41.3.489
10.1006/jmaa.1994.1277
10.1016/j.jmaa.2005.11.067
10.1016/j.jmaa.2007.01.114
10.1016/j.aml.2006.02.014
10.1016/0362-546X(80)90085-1
10.1023/B:JOTA.0000026271.19947.05
10.1002/mana.19861290121
ContentType Journal Article
Copyright 2009 Elsevier B.V.
Copyright_xml – notice: 2009 Elsevier B.V.
DBID AAYXX
CITATION
7SC
7TB
8FD
FR3
JQ2
KR7
L7M
L~C
L~D
DOI 10.1016/j.cnsns.2009.03.037
DatabaseName CrossRef
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
ProQuest Computer Science Collection
Civil Engineering Abstracts
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Civil Engineering Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList
Civil Engineering Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
EISSN 1878-7274
EndPage 251
ExternalDocumentID 10_1016_j_cnsns_2009_03_037
S1007570409001841
GroupedDBID --K
--M
-01
-0A
-0I
-0Y
-SA
-S~
.~1
0R~
1B1
1RT
1~.
1~5
29F
4.4
457
4G.
5GY
5VR
5VS
7-5
71M
8P~
92M
9D9
9DA
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
ABAOU
ABFNM
ABJNI
ABMAC
ABNEU
ABXDB
ABYKQ
ACAZW
ACDAQ
ACFVG
ACGFS
ACNNM
ACRLP
ADBBV
ADEZE
ADGUI
ADMUD
ADTZH
AEBSH
AECPX
AEKER
AENEX
AFKWA
AFTJW
AFUIB
AGHFR
AGUBO
AGYEJ
AHJVU
AIEXJ
AIGVJ
AIKHN
AITUG
AIVDX
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CAJEA
CAJUS
CCEZO
CCVFK
CHBEP
CS3
CUBFJ
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
FA0
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-Q
GBLVA
HVGLF
HZ~
IHE
J1W
JJJVA
JUIAU
KOM
M41
MHUIS
MO0
N9A
O-L
O9-
OAUVE
OGIMB
OZT
P-8
P-9
P2P
PC.
Q--
Q-0
Q38
R-A
R-I
R2-
RIG
ROL
RPZ
RT1
RT9
S..
SDF
SDG
SES
SEW
SPC
SPCBC
SPD
SSQ
SST
SSW
SSZ
T5K
T8Q
T8Y
U1F
U1G
U5A
U5I
U5K
UHS
~G-
~LA
AATTM
AAXKI
AAYWO
AAYXX
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
7SC
7TB
8FD
FR3
JQ2
KR7
L7M
L~C
L~D
ID FETCH-LOGICAL-c334t-7795243ab8d8a10a33dc53d4477d77e254eac173ea3915e4ddd43547ff0bf5573
IEDL.DBID AIKHN
ISSN 1007-5704
IngestDate Thu Oct 02 07:36:36 EDT 2025
Wed Oct 01 02:51:04 EDT 2025
Thu Apr 24 23:11:30 EDT 2025
Fri Feb 23 02:30:01 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords RMM models
Hybrid algorithms
47H10
System of nonlinear set-valued variational inclusions
( A,η) -maximal relaxed monotone mapping
49J40
Yosida approximations
Generalized resolvent operator method
65B05
Yosida regularizations
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c334t-7795243ab8d8a10a33dc53d4477d77e254eac173ea3915e4ddd43547ff0bf5573
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
PQID 34752204
PQPubID 23500
PageCount 14
ParticipantIDs proquest_miscellaneous_34752204
crossref_primary_10_1016_j_cnsns_2009_03_037
crossref_citationtrail_10_1016_j_cnsns_2009_03_037
elsevier_sciencedirect_doi_10_1016_j_cnsns_2009_03_037
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2010-02-01
PublicationDateYYYYMMDD 2010-02-01
PublicationDate_xml – month: 02
  year: 2010
  text: 2010-02-01
  day: 01
PublicationDecade 2010
PublicationTitle Communications in nonlinear science & numerical simulation
PublicationYear 2010
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Cho, P Fang, Huang, Hwang (bib3) 2004; 41
R.U. Verma, On the generalized proximal point algorithm with applications to inclusion problems, Journal of Industrial and Management Optimization doi:10.3934/jimo.2009.5.xx
Nadler (bib16) 1969; 30
Huang, Fang (bib9) 2003; 62
Verma (bib18) 2004; 17
Zeidler (bib33) 1980; 4
R.U. Verma, Generalized Rockafellar’s theorem on linear convergence, Nonlinear Functional Analysis and Applications, in press.
Zeidler (bib35) 1986; vol. I
Verma (bib29) 2009; 10
Ding, Luo (bib4) 2000; 210
maximal accretiveness framework in Banach spaces, Positivity doi 10.1007/s11117-00822.68-6.
Fang, Huang (bib6) 2004; 11
Kazmi (bib13) 1997; 209
Verma (bib24) 2007; 49
Zhu, Marcotte (bib38) 1996; 6
Jin, Liu (bib11) 2004; 9
Fang, Huang (bib5) 2003; 145
Hassouni, Moudafi (bib8) 1994; 185
Jin (bib12) 2004; 7
Verma (bib23) 2008; 12
Verma (bib28) 2009; 12
Agarwal, Huang, Cho (bib1) 2002; 7
Yosida (bib32) 1965
Zeidler (bib34) 1986; 129
Verma (bib31) 2009; 22
Verma (bib17) 2004; 121
Verma (bib19) 2004; 8
Verma (bib20) 2006; 129
Zeidler (bib37) 1985; vol. III
R.U. Verma, General proximal point algorithm involving
Jin (bib10) 2006; 7
Kim, Kim (bib14) 2004; 11
R.U. Verma, Approximation solvability of a class of nonlinear set-valued variational inclusions involving
Verma (bib21) 2006; 19
Zeidler (bib36) 1990; vol. II/B
Lan, Kim, Cho (bib15) 2007; 327
Chang, Cho, Zhou (bib2) 2002
Fang, Huang, Thompson (bib7) 2005; 49
monotone mappings, Journal of Mathematical Analysis and Applications 337(2008) 969–975.
Verma (bib25) 1994
Verma (10.1016/j.cnsns.2009.03.037_bib25) 1994
Jin (10.1016/j.cnsns.2009.03.037_bib10) 2006; 7
Kim (10.1016/j.cnsns.2009.03.037_bib14) 2004; 11
Verma (10.1016/j.cnsns.2009.03.037_bib28) 2009; 12
Nadler (10.1016/j.cnsns.2009.03.037_bib16) 1969; 30
Verma (10.1016/j.cnsns.2009.03.037_bib19) 2004; 8
Zhu (10.1016/j.cnsns.2009.03.037_bib38) 1996; 6
10.1016/j.cnsns.2009.03.037_bib30
Verma (10.1016/j.cnsns.2009.03.037_bib17) 2004; 121
Verma (10.1016/j.cnsns.2009.03.037_bib31) 2009; 22
Hassouni (10.1016/j.cnsns.2009.03.037_bib8) 1994; 185
Zeidler (10.1016/j.cnsns.2009.03.037_bib33) 1980; 4
Jin (10.1016/j.cnsns.2009.03.037_bib12) 2004; 7
Chang (10.1016/j.cnsns.2009.03.037_bib2) 2002
Verma (10.1016/j.cnsns.2009.03.037_bib24) 2007; 49
Zeidler (10.1016/j.cnsns.2009.03.037_bib35) 1986; vol. I
Zeidler (10.1016/j.cnsns.2009.03.037_bib36) 1990; vol. II/B
Verma (10.1016/j.cnsns.2009.03.037_bib23) 2008; 12
Fang (10.1016/j.cnsns.2009.03.037_bib5) 2003; 145
Yosida (10.1016/j.cnsns.2009.03.037_bib32) 1965
Zeidler (10.1016/j.cnsns.2009.03.037_bib37) 1985; vol. III
Verma (10.1016/j.cnsns.2009.03.037_bib29) 2009; 10
Jin (10.1016/j.cnsns.2009.03.037_bib11) 2004; 9
Zeidler (10.1016/j.cnsns.2009.03.037_bib34) 1986; 129
10.1016/j.cnsns.2009.03.037_bib26
Cho (10.1016/j.cnsns.2009.03.037_bib3) 2004; 41
Ding (10.1016/j.cnsns.2009.03.037_bib4) 2000; 210
Fang (10.1016/j.cnsns.2009.03.037_bib6) 2004; 11
Verma (10.1016/j.cnsns.2009.03.037_bib18) 2004; 17
Lan (10.1016/j.cnsns.2009.03.037_bib15) 2007; 327
10.1016/j.cnsns.2009.03.037_bib22
Agarwal (10.1016/j.cnsns.2009.03.037_bib1) 2002; 7
Verma (10.1016/j.cnsns.2009.03.037_bib20) 2006; 129
Huang (10.1016/j.cnsns.2009.03.037_bib9) 2003; 62
10.1016/j.cnsns.2009.03.037_bib27
Kazmi (10.1016/j.cnsns.2009.03.037_bib13) 1997; 209
Verma (10.1016/j.cnsns.2009.03.037_bib21) 2006; 19
Fang (10.1016/j.cnsns.2009.03.037_bib7) 2005; 49
References_xml – volume: 185
  start-page: 706
  year: 1994
  end-page: 712
  ident: bib8
  article-title: A perturbed algorithms for variational inequalities
  publication-title: J Math Anal Appl
– volume: 6
  start-page: 714
  year: 1996
  end-page: 726
  ident: bib38
  article-title: Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities
  publication-title: SIAM J Optim
– volume: 41
  start-page: 489
  year: 2004
  end-page: 499
  ident: bib3
  article-title: Algorithms for systems of nonlinear variational inequalities
  publication-title: J Korean Math Soc
– volume: 209
  start-page: 572
  year: 1997
  end-page: 584
  ident: bib13
  article-title: Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions
  publication-title: J Math Anal Appl
– volume: 49
  start-page: 205
  year: 2007
  end-page: 212
  ident: bib24
  article-title: General projection systems and relaxed cocoercive nonlinear variational inequalities
  publication-title: ANZIAM J (Aust Math Soc)
– year: 2002
  ident: bib2
  article-title: Iterative Methods for Nonlinear Operator Equations in Banach Spaces
– volume: vol. III
  year: 1985
  ident: bib37
  publication-title: Nonlinear functional analysis and its applications
– volume: 49
  start-page: 365
  year: 2005
  end-page: 374
  ident: bib7
  article-title: A new system of variational inclusions with
  publication-title: Comput Math Appl
– volume: 19
  start-page: 1409
  year: 2006
  end-page: 1413
  ident: bib21
  article-title: Sensitivity analysis for generalized strongly monotone variational inclusions based on
  publication-title: Appl Math Lett
– year: 1994
  ident: bib25
  article-title: Nonlinear Approximation solvability Involving Regular and Demiregular Convergence
– volume: 9
  start-page: 485
  year: 2004
  end-page: 494
  ident: bib11
  article-title: Nonlinear quasi-variational inclusions involving generalized m-accretive mappings
  publication-title: Nonlinear Funct Anal Appl
– volume: 7
  start-page: 807
  year: 2002
  end-page: 828
  ident: bib1
  article-title: Generalized nonlinear mixed implicit quasi-variational inclusions with set-valued mappings
  publication-title: J Inequalities Appl
– reference: R.U. Verma, Generalized Rockafellar’s theorem on linear convergence, Nonlinear Functional Analysis and Applications, in press.
– volume: 12
  start-page: 73
  year: 2009
  end-page: 99
  ident: bib28
  article-title: General nonlinear variational inclusion systems involving A-maximal
  publication-title: Adv Nonlinear Variational Inequalities
– volume: 145
  start-page: 795
  year: 2003
  end-page: 803
  ident: bib5
  article-title: H-Monotone operator and resolvent operator technique for variational inclusions
  publication-title: Appl Math Comput
– volume: 4
  start-page: 451
  year: 1980
  end-page: 489
  ident: bib33
  article-title: The Ljusternik-Schirelman theory for indefinite and not necessarily odd nonlinear operators and its applications
  publication-title: Nonlinear Anal: Theory Method Appl
– volume: 22
  start-page: 698
  year: 2009
  end-page: 703
  ident: bib31
  article-title: General framework for the over-relaxed A-proximal point algorithm and applications to inclusion problems
  publication-title: Appl Math Lett
– volume: 210
  start-page: 153
  year: 2000
  end-page: 165
  ident: bib4
  article-title: Perturbed proximal point algorithms for generalized quasi-variational-like inclusions
  publication-title: J Comput Appl Math
– volume: 327
  start-page: 481
  year: 2007
  end-page: 493
  ident: bib15
  article-title: On a new system of nonlinear A-monotone multivalued variational inclusions
  publication-title: J Math Anal Appl
– volume: vol. II/B
  year: 1990
  ident: bib36
  publication-title: Nonlinear functional analysis and its applications
– volume: 11
  start-page: 117
  year: 2004
  end-page: 124
  ident: bib14
  article-title: A new system of generalized nonlinear mixed variational inequalities in Hilbert spaces
  publication-title: J Convex Anal
– reference: R.U. Verma, General proximal point algorithm involving
– volume: 17
  start-page: 193
  year: 2004
  end-page: 195
  ident: bib18
  article-title: A-monotonicity and applications to nonlinear variational inclusions
  publication-title: J Appl Math Stochastic Anal
– reference: R.U. Verma, On the generalized proximal point algorithm with applications to inclusion problems, Journal of Industrial and Management Optimization doi:10.3934/jimo.2009.5.xx
– volume: vol. I
  year: 1986
  ident: bib35
  publication-title: Nonlinear functional analysis and its applications
– volume: 30
  start-page: 475
  year: 1969
  end-page: 488
  ident: bib16
  article-title: Multi-valued contraction mappings
  publication-title: Pacific J Math
– year: 1965
  ident: bib32
  article-title: Functional Analysis
– volume: 11
  start-page: 93
  year: 2004
  end-page: 101
  ident: bib6
  article-title: H-monotone operators and system of variational inclusions
  publication-title: Commun Appl Nonlinear Anal
– reference: R.U. Verma, Approximation solvability of a class of nonlinear set-valued variational inclusions involving
– volume: 10
  start-page: 185
  year: 2009
  end-page: 195
  ident: bib29
  article-title: The over-relaxed A-proximal point algorithm and applications to nonlinear variational inclusions in Banach spaces
  publication-title: Fixed Point Theory
– volume: 8
  start-page: 55
  year: 2004
  end-page: 66
  ident: bib19
  article-title: Approximation-solvability of a class of A-monotone variational inclusion problems
  publication-title: J Korean Soc Indus Appl Math
– reference: -monotone mappings, Journal of Mathematical Analysis and Applications 337(2008) 969–975.
– volume: 62
  start-page: 83
  year: 2003
  end-page: 98
  ident: bib9
  article-title: A new class of general variational inclusions involving maximal
  publication-title: Publ Math Debrecen
– volume: 7
  year: 2006
  ident: bib10
  article-title: Iterative algorithm for a new system of nonlinear set-valued variational inclusions involving
  publication-title: J Inequalities Pure Appl Math
– volume: 7
  start-page: 173
  year: 2004
  end-page: 181
  ident: bib12
  article-title: Generalized nonlinear implicit quasi-variational inclusions with relaxed monotone mappings
  publication-title: Adv Nonlinear Variational Inequalities
– reference: -maximal accretiveness framework in Banach spaces, Positivity doi 10.1007/s11117-00822.68-6.
– volume: 12
  start-page: 192
  year: 2008
  end-page: 201
  ident: bib23
  article-title: Nonlinear variational inclusion problems for sensitivity analysis based on RMM mappings
  publication-title: Math Sci Res J
– volume: 129
  start-page: 235
  year: 1986
  end-page: 259
  ident: bib34
  article-title: Ljusternik–Schirelman theory on general level sets
  publication-title: Math Nachr
– volume: 121
  start-page: 203
  year: 2004
  end-page: 210
  ident: bib17
  article-title: Generalized system for relaxed coercive variational inequalities and projection methods
  publication-title: J Optim Theory Appl
– volume: 129
  start-page: 457
  year: 2006
  end-page: 467
  ident: bib20
  article-title: A-monotonicity and its role in nonlinear variational inclusions
  publication-title: J Optim Theory Appl
– volume: 17
  start-page: 193
  issue: 2
  year: 2004
  ident: 10.1016/j.cnsns.2009.03.037_bib18
  article-title: A-monotonicity and applications to nonlinear variational inclusions
  publication-title: J Appl Math Stochastic Anal
  doi: 10.1155/S1048953304403013
– ident: 10.1016/j.cnsns.2009.03.037_bib27
– volume: 22
  start-page: 698
  year: 2009
  ident: 10.1016/j.cnsns.2009.03.037_bib31
  article-title: General framework for the over-relaxed A-proximal point algorithm and applications to inclusion problems
  publication-title: Appl Math Lett
  doi: 10.1016/j.aml.2008.05.001
– volume: 49
  start-page: 365
  year: 2005
  ident: 10.1016/j.cnsns.2009.03.037_bib7
  article-title: A new system of variational inclusions with ( H,η) -monotone operators in Hilbert spaces
  publication-title: Comput Math Appl
  doi: 10.1016/j.camwa.2004.04.037
– volume: vol. I
  year: 1986
  ident: 10.1016/j.cnsns.2009.03.037_bib35
– volume: 11
  start-page: 93
  issue: 1
  year: 2004
  ident: 10.1016/j.cnsns.2009.03.037_bib6
  article-title: H-monotone operators and system of variational inclusions
  publication-title: Commun Appl Nonlinear Anal
– volume: 6
  start-page: 714
  year: 1996
  ident: 10.1016/j.cnsns.2009.03.037_bib38
  article-title: Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities
  publication-title: SIAM J Optim
  doi: 10.1137/S1052623494250415
– volume: 209
  start-page: 572
  year: 1997
  ident: 10.1016/j.cnsns.2009.03.037_bib13
  article-title: Mann and Ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions
  publication-title: J Math Anal Appl
  doi: 10.1006/jmaa.1997.5368
– volume: vol. III
  year: 1985
  ident: 10.1016/j.cnsns.2009.03.037_bib37
– volume: 10
  start-page: 185
  issue: 1
  year: 2009
  ident: 10.1016/j.cnsns.2009.03.037_bib29
  article-title: The over-relaxed A-proximal point algorithm and applications to nonlinear variational inclusions in Banach spaces
  publication-title: Fixed Point Theory
– volume: 7
  start-page: 807
  issue: 6
  year: 2002
  ident: 10.1016/j.cnsns.2009.03.037_bib1
  article-title: Generalized nonlinear mixed implicit quasi-variational inclusions with set-valued mappings
  publication-title: J Inequalities Appl
– volume: 62
  start-page: 83
  year: 2003
  ident: 10.1016/j.cnsns.2009.03.037_bib9
  article-title: A new class of general variational inclusions involving maximal η-monotone mappings
  publication-title: Publ Math Debrecen
  doi: 10.5486/PMD.2003.2629
– volume: 49
  start-page: 205
  year: 2007
  ident: 10.1016/j.cnsns.2009.03.037_bib24
  article-title: General projection systems and relaxed cocoercive nonlinear variational inequalities
  publication-title: ANZIAM J (Aust Math Soc)
– volume: 7
  issue: 2
  year: 2006
  ident: 10.1016/j.cnsns.2009.03.037_bib10
  article-title: Iterative algorithm for a new system of nonlinear set-valued variational inclusions involving ( H,η) -monotone mappings
  publication-title: J Inequalities Pure Appl Math
– year: 2002
  ident: 10.1016/j.cnsns.2009.03.037_bib2
– volume: 30
  start-page: 475
  year: 1969
  ident: 10.1016/j.cnsns.2009.03.037_bib16
  article-title: Multi-valued contraction mappings
  publication-title: Pacific J Math
  doi: 10.2140/pjm.1969.30.475
– volume: 145
  start-page: 795
  year: 2003
  ident: 10.1016/j.cnsns.2009.03.037_bib5
  article-title: H-Monotone operator and resolvent operator technique for variational inclusions
  publication-title: Appl Math Comput
– volume: 129
  start-page: 457
  issue: 3
  year: 2006
  ident: 10.1016/j.cnsns.2009.03.037_bib20
  article-title: A-monotonicity and its role in nonlinear variational inclusions
  publication-title: J Optim Theory Appl
  doi: 10.1007/s10957-006-9079-7
– volume: 210
  start-page: 153
  year: 2000
  ident: 10.1016/j.cnsns.2009.03.037_bib4
  article-title: Perturbed proximal point algorithms for generalized quasi-variational-like inclusions
  publication-title: J Comput Appl Math
  doi: 10.1016/S0377-0427(99)00250-2
– volume: 7
  start-page: 173
  issue: 2
  year: 2004
  ident: 10.1016/j.cnsns.2009.03.037_bib12
  article-title: Generalized nonlinear implicit quasi-variational inclusions with relaxed monotone mappings
  publication-title: Adv Nonlinear Variational Inequalities
– volume: vol. II/B
  year: 1990
  ident: 10.1016/j.cnsns.2009.03.037_bib36
– volume: 12
  start-page: 73
  issue: 1
  year: 2009
  ident: 10.1016/j.cnsns.2009.03.037_bib28
  article-title: General nonlinear variational inclusion systems involving A-maximal ( m) -relaxed monotone, RMM, RMRM,PSM and cocoercive mappings
  publication-title: Adv Nonlinear Variational Inequalities
– volume: 9
  start-page: 485
  issue: 3
  year: 2004
  ident: 10.1016/j.cnsns.2009.03.037_bib11
  article-title: Nonlinear quasi-variational inclusions involving generalized m-accretive mappings
  publication-title: Nonlinear Funct Anal Appl
– ident: 10.1016/j.cnsns.2009.03.037_bib30
– volume: 11
  start-page: 117
  year: 2004
  ident: 10.1016/j.cnsns.2009.03.037_bib14
  article-title: A new system of generalized nonlinear mixed variational inequalities in Hilbert spaces
  publication-title: J Convex Anal
– volume: 41
  start-page: 489
  year: 2004
  ident: 10.1016/j.cnsns.2009.03.037_bib3
  article-title: Algorithms for systems of nonlinear variational inequalities
  publication-title: J Korean Math Soc
  doi: 10.4134/JKMS.2004.41.3.489
– ident: 10.1016/j.cnsns.2009.03.037_bib26
– volume: 185
  start-page: 706
  year: 1994
  ident: 10.1016/j.cnsns.2009.03.037_bib8
  article-title: A perturbed algorithms for variational inequalities
  publication-title: J Math Anal Appl
  doi: 10.1006/jmaa.1994.1277
– volume: 327
  start-page: 481
  year: 2007
  ident: 10.1016/j.cnsns.2009.03.037_bib15
  article-title: On a new system of nonlinear A-monotone multivalued variational inclusions
  publication-title: J Math Anal Appl
  doi: 10.1016/j.jmaa.2005.11.067
– ident: 10.1016/j.cnsns.2009.03.037_bib22
  doi: 10.1016/j.jmaa.2007.01.114
– year: 1965
  ident: 10.1016/j.cnsns.2009.03.037_bib32
– volume: 12
  start-page: 192
  year: 2008
  ident: 10.1016/j.cnsns.2009.03.037_bib23
  article-title: Nonlinear variational inclusion problems for sensitivity analysis based on RMM mappings
  publication-title: Math Sci Res J
– volume: 19
  start-page: 1409
  year: 2006
  ident: 10.1016/j.cnsns.2009.03.037_bib21
  article-title: Sensitivity analysis for generalized strongly monotone variational inclusions based on ( A,η) -resolvent operator technique
  publication-title: Appl Math Lett
  doi: 10.1016/j.aml.2006.02.014
– volume: 4
  start-page: 451
  year: 1980
  ident: 10.1016/j.cnsns.2009.03.037_bib33
  article-title: The Ljusternik-Schirelman theory for indefinite and not necessarily odd nonlinear operators and its applications
  publication-title: Nonlinear Anal: Theory Method Appl
  doi: 10.1016/0362-546X(80)90085-1
– volume: 8
  start-page: 55
  issue: 1
  year: 2004
  ident: 10.1016/j.cnsns.2009.03.037_bib19
  article-title: Approximation-solvability of a class of A-monotone variational inclusion problems
  publication-title: J Korean Soc Indus Appl Math
– year: 1994
  ident: 10.1016/j.cnsns.2009.03.037_bib25
– volume: 121
  start-page: 203
  year: 2004
  ident: 10.1016/j.cnsns.2009.03.037_bib17
  article-title: Generalized system for relaxed coercive variational inequalities and projection methods
  publication-title: J Optim Theory Appl
  doi: 10.1023/B:JOTA.0000026271.19947.05
– volume: 129
  start-page: 235
  year: 1986
  ident: 10.1016/j.cnsns.2009.03.037_bib34
  article-title: Ljusternik–Schirelman theory on general level sets
  publication-title: Math Nachr
  doi: 10.1002/mana.19861290121
SSID ssj0016954
Score 2.0700092
Snippet In this paper, a new system of nonlinear (set-valued) variational inclusions involving ( A,η) -maximal relaxed monotone and relative ( A,η) -maximal monotone...
In this paper, a new system of nonlinear (set-valued) variational inclusions involving (A,[eta])-maximal relaxed monotone and relative (A,[eta])-maximal...
SourceID proquest
crossref
elsevier
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 238
SubjectTerms 47H10
49J40
65B05
[formula omitted]-maximal relaxed monotone mapping
Generalized resolvent operator method
Hybrid algorithms
RMM models
System of nonlinear set-valued variational inclusions
Yosida approximations
Yosida regularizations
Title General system of ( A,η) -maximal relaxed monotone variational inclusion problems based on generalized hybrid algorithms
URI https://dx.doi.org/10.1016/j.cnsns.2009.03.037
https://www.proquest.com/docview/34752204
Volume 15
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier ScienceDirect
  customDbUrl:
  eissn: 1878-7274
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0016954
  issn: 1007-5704
  databaseCode: .~1
  dateStart: 19960101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals [SCFCJ]
  customDbUrl:
  eissn: 1878-7274
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0016954
  issn: 1007-5704
  databaseCode: AIKHN
  dateStart: 19960101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: SD Complete Freedom Collection
  customDbUrl:
  eissn: 1878-7274
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0016954
  issn: 1007-5704
  databaseCode: ACRLP
  dateStart: 19960101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVLSH
  databaseName: Elsevier Journals
  customDbUrl:
  mediaType: online
  eissn: 1878-7274
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0016954
  issn: 1007-5704
  databaseCode: AKRWK
  dateStart: 19960101
  isFulltext: true
  providerName: Library Specific Holdings
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnR1NS8MwNOh28eK3-G0OHhSsW5d0aY9DlKm4iwreSpo0Wtm6sW6iguLVX-S_8Ef4S3yvTQUFPQiB0iQvhLzkfSTvg5BtA6dIGxe0E2OMw5uSO75UyvHciIsAWZzGe8izTrN9yU-uvKsJclD6wqBZpaX9BU3PqbWtqdnVrA2SpHaO7_uegE0YYGY5dF6vAv_x_Qqpto5P252vx4RmkCdDw_4OApTBh3IzL5VmaWbjVjIo4jcG9YNU5_znaJZMW8GRtoq5zZGJOJ0nM1aIpPaIZgvkyQaSpkWMZto3dOfj5bW19_62C1-nJ--THjSjE8s9QMI27GNAbnoHWrO9GaRJqrpjvEejNuFMRpHdaQo118X4ySP83jygwxeV3ev-MBnd9LJFcnl0eHHQdmyOBUcxxkcgXAdegzMZ-dqXbl0yphVgj3MhtBAxqI9AmV3BYomR5GOutQYBiwtj6pHxPMGWSCWFSS4TGqgGtMeg8YJYYGBBjYwipUB_8bXknlghjXJhQ2UDkGMejG5YWprdhjk2MDVmENYZFADa-wIaFPE3_u7eLDEWfttGIXCIvwG3SvyGcMDw1USmcX-chYwLkFHrfPW_Q6-RqcLkAG1g1kllNBzHGyDJjKJNMrn_7G7a_foJrUj31A
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnR3LSgMxMIge9OJbfJuDBwXXdpts0z0WUerzooK3kE02dqXdittKFRSvfpF_4Uf4Jc7sZgUFPQiBZfMiZCbzSOZByKaFU2SsD9qJtdbjdcW9htLaC_yIixBZnMF7yNOzeuuSH10FVyNkr_SFQbNKR_sLmp5Ta1dTcbtZuU2Syjm-7wcCkDDEzHLovD7Gg5pADWz3-cvOw6-HeSo07O1h9zL0UG7kpdMszVzUSgZF_MaefhDqnPscTJNJJzbSZrGyGTISp7NkyomQ1B3QbI48uTDStIjQTHuWbn28vDZ33t-24et11TDpQjO6sAxhJCBhD8Nx03vQmd29IE1S3RngLRp16WYyiszOUKi5LuZPHuG3_YDuXlR1rnt3Sb_dzebJ5cH-xV7LcxkWPM0Y74NoHQY1zlTUMA3lVxVjRgPsOBfCCBGD8gh02RcsVhhHPubGGBCvuLC2GtkgEGyBjKawyEVCQ12D9hj0XRAKLGyoVVGkNWgvDaN4IJZIrdxYqV34ccyC0ZGlndmNzKGBiTFDWWVQYNDO16DbIvrG393rJcTkNySSwB_-HrhRwlfC8cI3E5XGvUEmGRcgoVb58n-n3iDjrYvTE3lyeHa8QiYK4wO0hlklo_27QbwGMk0_Ws9x9hPHYPic
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=General+system+of+%28A%2C%5Beta%5D%29-maximal+relaxed+monotone+variational+inclusion+problems+based+on+generalized+hybrid+algorithms&rft.jtitle=Communications+in+nonlinear+science+%26+numerical+simulation&rft.au=Agarwal%2C+Ravi+P&rft.au=Verma%2C+Ram+U&rft.date=2010-02-01&rft.issn=1007-5704&rft.volume=15&rft.issue=2&rft.spage=238&rft.epage=251&rft_id=info:doi/10.1016%2Fj.cnsns.2009.03.037&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1007-5704&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1007-5704&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1007-5704&client=summon