A new inertial algorithm for equilibrium problem and a family of nonexpansive operators in Hilbert space

In this article, we suggest and study a new inertial algorithm combining inertial extrapolation, S‐iteration process and viscosity approximation method for computing a common solution of an equilibrium problem and a family of nonexpansive operators in real Hilbert space. We provide a strong converge...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 48; no. 7; pp. 7950 - 7961
Main Author Asad, Mohd
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 15.05.2025
Subjects
Algorithms
equilibrium problem
Hilbert space
inertial extrapolation
nonexpansive mapping
Operators
S‐iteration method
viscosity approximation method
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ISSN0170-4214
1099-1476
DOI10.1002/mma.9447

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Summary:In this article, we suggest and study a new inertial algorithm combining inertial extrapolation, S‐iteration process and viscosity approximation method for computing a common solution of an equilibrium problem and a family of nonexpansive operators in real Hilbert space. We provide a strong convergence result of the suggested algorithm under some simple assumptions on control sequences. Further, we compare our suggested algorithm with some existing well‐known algorithms by an analytical example. Some prominent recent findings in this field have been improved, generalized, and extended as an outcome of this paper.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9447