Parallel Hybrid Algorithm for Solving Pseudomonotone Equilibrium and Split Common Fixed Point Problems

A. Taiwo, L. O. Jolaoso, O. T. Mewomo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)

Abstract

Using the concept of Bregman W-mapping, we propose a parallel hybrid extragradient algorithm for approximating a common element of the set of solutions of pseudomonotone equilibrium problems and split common fixed point problems of Bregman weak relatively nonexpansive mappings. With the algorithm, we state and prove a strong convergence result for finding a common solution of finite family of equilibrium problem and split common fixed point problem in a real Banach space. The stepsize for the split common fixed point problem is chosen in such a way that the algorithm does not require a prior estimation of the operator norm. Finally, we present an application of our results to variational inequality problems. Our result improves and extends some existing results in the literature in these directions.

Original languageEnglish
Pages (from-to)1893-1918
Number of pages26
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume43
Issue number2
DOIs
Publication statusPublished - 1 Mar 2020
Externally publishedYes

Keywords

  • Bregman W-mapping
  • Hybrid extragradient method
  • Pseudomonotone equilibrium problem
  • Split common fixed point problem

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