A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces

Authors:
Yekini Shehu
Affiliations:
Mathematics Institute, African University of Science and Technology, Abuja, Nigeria
Venue:
Journal of Global Optimization
Year:
2012

Citing 8
Cited 0

Strong Convergence of a Proximal-Type Algorithm in a Banach Space

SIAM Journal on Optimization
An Outer Approximation Method for the Variational Inequality Problem

SIAM Journal on Control and Optimization
Variational inclusions with a general H-monotone operator in Banach spaces

Computers & Mathematics with Applications
Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space

Journal of Approximation Theory
Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces

Journal of Computational and Applied Mathematics
A strong convergence theorem for relatively nonexpansive mappings in a Banach space

Journal of Approximation Theory
Strong convergence theorems for relatively nonexpansive mappings in Banach spaces with applications

Computers & Mathematics with Applications
Korpelevich's method for variational inequality problems in Banach spaces

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we construct a new iterative scheme and prove strong convergence theorem for approximation of a common fixed point of a countable family of relatively nonexpansive mappings, which is also a solution to an equilibrium problem in a uniformly convex and uniformly smooth real Banach space. We apply our results to approximate fixed point of a nonexpansive mapping, which is also solution to an equilibrium problem in a real Hilbert space and prove strong convergence of general H-monotone mappings in a uniformly convex and uniformly smooth real Banach space. Our results extend many known recent results in the literature.