A modified iterative algorithm for split feasibility problems of right Bregman strongly quasi-nonexpansive mappings in Banach spaces with applications
type: Item
instance of: scholarly article
title: A modified iterative algorithm for split feasibility problems of right Bregman strongly quasi-nonexpansive mappings in Banach spaces with applications
zbMATH Open document ID: 1466.47046
author: Anantachai Padcharoen
author: Poom Kumam
author: Yeol Je Cho
author: Phatiphat Thounthong
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: In this paper, we present a new iterative scheme for finding a common element of the solution set \(\mathcal F\) of the split feasibility problem and the fixed point set \(F(T)\) of a right Bregman strongly quasi-nonexpansive mapping \(T\) in \(p\)-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate conditions in real \(p\)-uniformly convex and uniformly smooth Banach spaces. Furthermore, we give some examples and applications to illustrate our main results in this paper. Our results extend and improve the recent ones of some others in the literature.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 7042384
zbMATH Keywords: right Bregman strongly quasi-nonexpansive
zbMATH Keywords: split feasibility problem
zbMATH Keywords: fixed point
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a9040075
OpenAlex ID: W2551947957
Wikidata QID: Q59306858
cites work: A multiprojection algorithm using Bregman projections in a product space
cites work: Iterative oblique projection onto convex sets and the split feasibility problem
cites work: Convergence theorem for equilibrium problem and Bregman strongly nonexpansive mappings in Banach spaces
cites work: A new multi-step iterative algorithm for approximating common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings
cites work: Further investigation into approximation of a common solution of fixed point problems and split feasibility problems
cites work: An iterative regularization method for the solution of the split feasibility problem in Banach spaces
cites work: A New Algorithm for Solving The Multiple-Sets Split Feasibility Problem in Banach Spaces
cites work: Convergence theorems for right Bregman strongly nonexpansive mappings in reflexive Banach spaces
cites work: Nonlinear functional analysis. Fixed point theory and its applications
cites work: Q3254057
cites work: Q3322631
cites work: An iterative row-action method for interval convex programming
cites work: Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
cites work: Convex functions, monotone operators and differentiability
cites work: Q5471308
cites work: Convergence analysis of an iterative algorithm for fixed point problems and split feasibility problems in certain Banach spaces
cites work: An iterative algorithm for solving split feasibility problems and fixed point problems in Banach spaces
cites work: Q4894797
cites work: Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces
cites work: Right Bregman nonexpansive operators in Banach spaces
cites work: Existence and Approximation of Fixed Points of Right Bregman Nonexpansive Operators
cites work: Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
cites work: Iterative Algorithms for Nonlinear Operators
DOI: 10.3390/A9040075
Recommended article: An inertial iterative algorithm with strong convergence for solving modified split feasibility problem in Banach spaces
Recommended article: Implicit iterative algorithms of the split common fixed point problem for Bregman quasi-nonexpansive mapping in Banach spaces
Recommended article: An iterative regularization method for the solution of the split feasibility problem in Banach spaces
Recommended article: A halpern-type iteration for solving the split feasibility problem and the fixed point problem of Bregman relatively nonexpansive semigroup in Banach spaces
Recommended article: An iterative algorithm for solving split feasibility problems and fixed point problems in Banach spaces
Recommended article: Generalized split feasibility problem for multi-valued Bregman quasi-nonexpansive mappings in Banach spaces
Recommended article: Iterative methods for the split feasibility problem and the fixed point problem in Banach spaces
Recommended article: An iterative algorithm for solving split equality fixed point problems for a class of nonexpansive-type mappings in Banach spaces
Recommended article: Q5253282
Recommended article: Strong convergence of hybrid Bregman projection algorithm for split feasibility and fixed point problems in Banach spaces
description: scientific article; zbMATH DE number 7042384