On Jc‐contraction and related fixed‐point problem with applications
We introduce Jc‐contraction, which encompasses both F‐contraction and JS‐contraction. We investigate a fixed‐point problem subject to Jc‐contraction. The existence of the solutions to the linear matrix equation and system of fractional differential equations are discussed by the application of obtai...
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          | Published in | Mathematical methods in the applied sciences Vol. 43; no. 17; pp. 10221 - 10236 | 
|---|---|
| Main Author | |
| Format | Journal Article | 
| Language | English | 
| Published | 
        Freiburg
          Wiley Subscription Services, Inc
    
        30.11.2020
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| Subjects | |
| Online Access | Get full text | 
| ISSN | 0170-4214 1099-1476  | 
| DOI | 10.1002/mma.6689 | 
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| Abstract | We introduce Jc‐contraction, which encompasses both F‐contraction and JS‐contraction. We investigate a fixed‐point problem subject to Jc‐contraction. The existence of the solutions to the linear matrix equation and system of fractional differential equations are discussed by the application of obtained results. | 
    
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| AbstractList | We introduce Jc‐contraction, which encompasses both F‐contraction and JS‐contraction. We investigate a fixed‐point problem subject to Jc‐contraction. The existence of the solutions to the linear matrix equation and system of fractional differential equations are discussed by the application of obtained results. | 
    
| Author | Nazam, Muhammad | 
    
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| Copyright | 2020 John Wiley & Sons, Ltd. | 
    
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| References_xml | – volume: 2014 start-page: 11 year: 2014 article-title: Some fixed point theorems concerning ‐contraction in complete dualistic partial metric spaces publication-title: Fixed Point Theory Appl – year: 1981 – volume: 132 start-page: 1435 year: 2003 end-page: 1443 article-title: A fixed point theorem in partially ordered sets and some applications to matrix equations publication-title: Proc Am Math Soc – volume: 10 start-page: 767 year: 2018 article-title: Relation theoretic (Θ,ℜ) contraction results with applications to nonlinear matrix equations publication-title: Symmetry – volume: 116 start-page: 708 issue: 8 year: 2009 end-page: 718 article-title: Partial metric spaces publication-title: Amer Math Monthly – volume: 2013 start-page: 83 year: 2013 article-title: On a nonlinear fractional differential equation on partially ordered metric spaces publication-title: Adv Differ Equ – year: 2000 – volume: 10 start-page: 383 issue: 2 year: 2016 end-page: 393 article-title: A unified version of Ran and Reurings theorem and Nieto and Rodra iguez‐LApezs theorem and low‐dimensional generalizations publication-title: Appl Math Inf Sci – volume: 18 start-page: 277 issue: 2 year: 2017 end-page: 287 article-title: Existence of common fixed points of improved ‐contraction on partial metric spaces publication-title: Appl Gen Topol – volume: 19 start-page: 1711 year: 2017 end-page: 1725 article-title: Fixed point theorems for F ‐contractions with applications to solution of nonlinear matrix equations publication-title: J Fixed Point Theory Appl – volume: 2011 start-page: 89 year: 2011 article-title: Solving systems of nonlinear matrix equations involving Lipschitzian mappings publication-title: Fixed Point Theory Appl – volume: 2013 start-page: 359 year: 2013 article-title: The existence of solutions for a nonlinear mixed problem of singular fractional differential equations publication-title: Adv Differ Equ – volume: 728 start-page: 183 year: 1995 end-page: 197 article-title: Partial metric topology publication-title: Ann New York Acad Sci – volume: 2019 start-page: 11 year: 2019 article-title: Common fixed point theorems for rational F ‐contractive pairs of mappings with applications publication-title: J Inequal Appl – volume: 371 year: 2013 article-title: Some existence results on nonlinear fractional differential equations publication-title: Philos Trans ‐ Royal Soc, Math Phys Eng Sci – volume: 160 start-page: 450 year: 2013 end-page: 454 article-title: Be careful on partial metric fixed point results publication-title: Topology and its Applications – volume: 25 start-page: 1638 year: 2012 end-page: 1643 article-title: Solving a class of matrix equations via the Bhaskar‐Lakshmikantham coupled fixed point theorem publication-title: Appl Math Lett – volume: 204 year: 2006 – volume: 2014 start-page: 439 year: 2014 article-title: Further generalizations of the Banach contraction principle publication-title: J Inequal Appl – volume: 134 start-page: 109705 year: 2020 article-title: A new study on the mathematical modelling of human liver with Caputo‐Fabrizio fractional derivative publication-title: Chaos, Solitons Fractals – volume: 2012 start-page: 94 year: 2012 article-title: Fixed points of a new type of contractive mappings in complete dualistic partial metric spaces publication-title: Fixed Point Theory Appl – year: 1997 – volume: 69 start-page: 126 issue: 2 year: 2017 end-page: 132 article-title: Towards cantor intersection theorem and Baire category theorem in partial metric spaces publication-title: Matematicki Vesnik – volume: 17 start-page: 693 issue: 4 year: 2015 end-page: 702 article-title: Relation‐theoretic contraction principle publication-title: Fixed Point Theory – volume: 9 start-page: 4127 year: 2016 end-page: 4136 article-title: Some fixed point theorems concerning ‐type contraction in complete metric spaces publication-title: J Nonlinear Sci Appl – volume: 2019 start-page: 79 year: 2019 article-title: On fractional integro‐differential inclusions via the extended fractional Caputo‐Fabrizio derivation publication-title: Boundary Value Problems – volume: 2020 start-page: 55 year: 2020 article-title: Analyzing transient response of the parallel RCL circuit by using the Caputo‐Fabrizio fractional derivative publication-title: Adv Differ Equ – volume: 2020 start-page: 71 year: 2020 article-title: Analysis of the model of HIV‐1 infection of T‐cell with a new approach of fractional derivative publication-title: Adv Differ Equ – volume: 2014 start-page: 38 year: 2014 article-title: A new generalization of the Banach contraction principle publication-title: J Inequal Appl  | 
    
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| Snippet | We introduce Jc‐contraction, which encompasses both F‐contraction and JS‐contraction. We investigate a fixed‐point problem subject to Jc‐contraction. The... | 
    
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| SubjectTerms | binary relation comparison function Differential equations fixed point Jc‐contraction Mathematical analysis matrix equation Matrix methods  | 
    
| Title | On Jc‐contraction and related fixed‐point problem with applications | 
    
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