On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces

H. A. Abass*, O. K. Oyewole, O. K. Narain, L. O. Jolaoso, B. I. Olajuwon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solution of split generalized equilibrium problem which is also a fixed point of Bregman relatively nonexpansive mapping in p-uniformly convex Banach spaces which are also uniformly smooth. Our iterative method uses step-size which does not require prior knowledge of the operator norm and we prove a strong convergence result under some mild conditions. We display a numerical example to illustrate the performance of our result. The result presented in this article unifies and extends several existing results in the literature.

Original languageEnglish
Article number416
JournalComputational and Applied Mathematics
Volume41
Issue number8
DOIs
Publication statusPublished - Dec 2022

Keywords

  • Bregman relatively nonexpansive mapping
  • Fixed point problem
  • Generalized equilibrium problem
  • Inertial method
  • Resolvent operators

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