In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for… (More)

Convergence theorem for common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings

N. Shahzad, H. Zegeye

Fixed Point Theory Appl

2014

Highly Influential

7 Excerpts

Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces

S. Reich, S. Sabach

Nonlinear Anal. TMA 2010,

2010

Highly Influential

4 Excerpts

Perturbation Analysis of Optimization Problems

J. F. Bonnans, A. Shapiro

2000

Highly Influential

4 Excerpts

The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming

L. M. Bregman

USSR Comput. Math. Math. Phys. 1967,

1967

Highly Influential

4 Excerpts

Metric and generalized projection operators in Banach spaces: Properties and applications

Y. I. Alber

ArXiv E-Prints

1996

Highly Influential

4 Excerpts

Strong convergence theorems for Bregman W-mappings with applications to convex feasibility problems in Banach spaces

E. Naraghirad, S. Timnak

Fixed Point Theory Appl. 2015,

2015

1 Excerpt

The modified Ishikawa iterative algorithm with errors for a countable family of Bregman totally quasi-D-asymptotically nonexpansive mappings in reflexive Banach spaces

Strong convergence results of two-steps modifying Halpernn’s iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application

@article{Kumam2016ANM,
title={A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings},
author={Wiyada Kumam and Pongsakorn Sunthrayuth and Phond Phunchongharn and Khajonpong Akkarajitsakul and Parinya Sa Ngiamsunthorn and Poom Kumam},
journal={Algorithms},
year={2016},
volume={9},
pages={37}
}