On split generalized equilibrium and fixed point problems of Bregman W-mappings with multiple output sets in reflexive Banach spaces

Abstract

In this paper, we introduce a Halpern iteration process for computing the common solution of split generalized equilibrium problem and fixed points of a countable family of Bregman W-mappings with multiple output sets in reflexive Banach spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. It is worth mentioning that the iterative algorithm employ in this article is designed in such a way that it does not require the prior knowledge of operator norm. We also provide some numerical examples to illustrate the performance of our proposed iterative method. The result discuss in this paper extends and complements many related results in literature.

Keywords

• Bregman weak relatively nonexpansive mapping
• Bregman W-mapping
• Halpern method
• iterative scheme
• split generalized equilibrium problem