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Algorithms 2016, 9(2), 37; doi:10.3390/a9020037

A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings

1
Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Rungsit-Nakorn Nayok Rd., Klong 6, Thanyaburi, Pathum Thani 12110, Thailand
2
Applied Computer Science Program, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
3
Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
4
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
*
Author to whom correspondence should be addressed.
Academic Editor: Jesper Jansson
Received: 3 December 2015 / Revised: 11 May 2016 / Accepted: 17 May 2016 / Published: 30 May 2016
View Full-Text   |   Download PDF [290 KB, uploaded 30 May 2016]

Abstract

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 the solution of variational inequality problems and to find the zero points of maximal monotone operators. The theorems furnished in this work are new and well-established and generalize many well-known recent research works in this field. View Full-Text
Keywords: common fixed point; multi-valued Bregman relatively nonexpansive mapping; strong convergence; iterative methods; reflexive Banach spaces; variational inequality problems; maximal monotone common fixed point; multi-valued Bregman relatively nonexpansive mapping; strong convergence; iterative methods; reflexive Banach spaces; variational inequality problems; maximal monotone
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Kumam, W.; Sunthrayuth, P.; Phunchongharn, P.; Akkarajitsakul, K.; Ngiamsunthorn, P.S.; Kumam, P. A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings. Algorithms 2016, 9, 37.

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