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

• Published in: Mathematical modelling and analysis Vol. 28; no. 4; pp. 653 - 672
• Main Authors: Abass, Hammed A., Ugwunnadi, Godwin C., Jolaoso, Lateef O., Narain, Ojen K.
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 20.10.2023
• Subjects: Applied mathematics; Banach spaces; Bregman W-mapping; Bregman weak relatively nonexpansive mapping; Equilibrium; Fixed point theory; Generalized estimating equations; Halpern method; Iterative algorithms; Iterative methods; iterative scheme; Mappings (Mathematics); split generalized equilibrium problem; Tests, problems and exercises; South Africa; split generalized equilibrium problem; Halpern method; Bregman W-mapping; iterative scheme; Bregman weak relatively nonexpansive mapping
• ISSN: 1392-6292; 1648-3510; 1648-3510
• DOI: 10.3846/mma.2023.17087

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.