Open access

DOI: 10.24193/fpt-ro.2018.1.26

Authors: F.U. Ogbuisi and O.T. Mewomo

Abstract: We introduce an iterative algorithm for approximating a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which is also a common solution of a finite system of generalized mixed equilibrium problems and a common zero of a finite family of maximal monotone operators in a reflexive real Banach space. A strong convergence theorem is also proved for finding an element in the intersection of the set of solution of a fixed point problem for infinite family of left Bregman strongly nonexpansive mappings, the set of solutions of a system of generalized mixed equilibrium problems and the set of zero points of a finite family of maximal monotone operators in a reflexive real Banach space. The result of this paper complement many related and important results in the literature.

Key Words and Phrases: Bregman distance, Bregman projection, maximal monotone operator, generalized mixed equilibrium problem, resolvent, Legendre function, reflexive real Banach space, zero point.

2010 Mathematics Subject Classification: 47H06, 47H09, 47J05, 47J25

Published on-line: February 1st, 2018.

Abstract pdf          Fulltext pdf

Back to volume's table of contents