Convergence theorem for system of pseudomonotone equilibrium and split common fixed point problems in Hilbert spaces

Lateef Olakunle Jolaoso*, Gafari Abiodun Lukumon, Maggie Aphane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider a system of pseudomonotone equilibrium problem and split common fixed point problem in the framework of real Hilbert spaces. We propose a modified extragradient method with line searching technique for approximating a common element in the sets of solutions of the two nonlinear problems. The convergence result is proved without prior knowledge of the Lipschitz-like constants of the equilibrium bifunctions and the norm of the bounded linear operator of the split common fixed point problem. We further provide some application and numerical example to show the importance of the obtained results in the paper.

Original languageEnglish
Pages (from-to)403-428
Number of pages26
JournalBolletino dell Unione Matematica Italiana
Volume14
Issue number2
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Demimetric mappings
  • Equilibrum problem
  • Parallel algorithm
  • Pseudomonotone equilibrium
  • Split common fixed point
  • numerical method

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