Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces

Authors:
Xiaolong Qin;Yeol Je Cho;Jung Im Kang;Shin Min Kang
Affiliations:
Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea;Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea;National Institute for Mathematical Sciences, 385-16, 3F Tower Koreana, Doryong-dong, Yuseong-gu, Daejeon 305-340, Republic of Korea;Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 5
Cited 5

On the convergence of Han's method for convex programming with quadratic objective

Mathematical Programming: Series A and B
Fixed point theorems for asymptotically nonexpansive mappings

Nonlinear Analysis: Theory, Methods & Applications
On Projection Algorithms for Solving Convex Feasibility Problems

SIAM Review
Approximation methods for common fixed points of infinite countable family of nonexpansive mappings

Computers & Mathematics with Applications
Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces

Computers & Mathematics with Applications

A composite iterative algorithm for common fixed points for a finite family of nonexpansive mappings and applications

Journal of Computational and Applied Mathematics
Strong convergence of the modified Ishikawa iterative method for infinitely many nonexpansive mappings in Banach spaces

Computers & Mathematics with Applications
Strong convergence theorems for solving equilibrium problems and fixed point problems of ξ-strict pseudo-contraction mappings by two hybrid projection methods

Journal of Computational and Applied Mathematics
Strong convergence of shrinking projection methods for quasi-φ-nonexpansive mappings and equilibrium problems

Journal of Computational and Applied Mathematics
A general iteration scheme for variational inequality problem and common fixed point problems of nonexpansive mappings in q-uniformly smooth Banach spaces

Journal of Global Optimization

Quantified Score

Hi-index	7.29

Visualization

Abstract

In an infinite-dimensional Hilbert space, the normal Mann's iteration algorithm has only weak convergence, in general, even for nonexpansive mappings. In order to get a strong convergence result, we modify the normal Mann's iterative process for an infinite family of nonexpansive mappings in the framework of Banach spaces. Our results improve and extend the recent results announced by many others.