A modified Halpern-type iterative method of a system of equilibrium problems and a fixed point for a totally quasi-\(\phi\)-asymptotically nonexpansive mapping in a Banach space
type: Item
instance of: scholarly article
title: A modified Halpern-type iterative method of a system of equilibrium problems and a fixed point for a totally quasi-\(\phi\)-asymptotically nonexpansive mapping in a Banach space
zbMATH Open document ID: 1323.47071
DOI: 10.1155/2012/750732
author: Preedaporn Kanjanasamranwong
author: Poom Kumam
author: Siwaporn Saewan
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized \(f\)-projection operator for finding a common solution of fixed-point problem of a totally quasi-\(\phi\)-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve the result of \textit{S. S. Chang} et al. [Appl. Math. Comput. 218, No.~11, 6489--6497 (2012; Zbl 1252.65097)] and some others.
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 6106304
zbMATH Keywords: modified Halpern-type method
zbMATH Keywords: generalized \(f\)-projection operator
zbMATH Keywords: totally quasi-\(\phi\)-asymptotically nonexpansive mapping
zbMATH Keywords: Kadec-Klee property
zbMATH Keywords: strong convergence
Wikidata QID: Q58907293
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/750732
OpenAlex ID: W2030163726
cites work: Mean Value Methods in Iteration
cites work: Projection and proximal point methods: Convergence results and counterexamples.
cites work: An example concerning fixed points
cites work: Fixed points of nonexpanding maps
cites work: Convergence of a modified Halpern-type iteration algorithm for quasi-\(\phi\)-nonexpansive mappings
cites work: A modified Halpern-type iteration algorithm for a family of hemi-relatively nonexpansive mappings and systems of equilibrium problems in Banach spaces
cites work: Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings
cites work: Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
cites work: Strong convergence theorems for relatively nonexpansive mappings in Banach spaces with applications
cites work: Convergence analysis for finite family of relatively quasi nonexpansive mappings and systems of equilibrium problems
cites work: A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications
cites work: Strong convergence theorems for relatively nonexpansive mappings in a Banach space
cites work: A modified Halpern-type iteration algorithm for totally quasi-\(\phi \)-asymptotically nonexpansive mappings with applications
cites work: Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces
cites work: Convergence theorems of a modified hybrid algorithm for a family of quasi-\(\varphi \)-asymptotically nonexpansive mappings
cites work: Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
cites work: Q4881794
cites work: Q3999276
cites work: Strong Convergence of a Proximal-Type Algorithm in a Banach Space
cites work: Nonlinear functional analysis. Fixed point theory and its applications
cites work: The generalised f-projection operator with an application
cites work: Q3322631
cites work: Approximative compactness and full rotundity in Musielak--Orlicz spaces and Lorentz--Orlicz spaces
cites work: Approximation theorems for total quasi-\(\phi \)-asymptotically nonexpansive mappings with applications
cites work: Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces
cites work: Q5185568
cites work: Q4366516
cites work: Existence and Approximation of Fixed Points of Firmly Nonexpansive-Type Mappings in Banach Spaces
description: scientific article; zbMATH DE number 6106304