A self-adaptive inertial subgradient extragradient method for pseudomonotone equilibrium and common fixed point problems

Lateef Olakunle Jolaoso*, Maggie Aphane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

In this paper, we introduce a self-adaptive inertial subgradient extragradient method for solving pseudomonotone equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm consists of an inertial extrapolation process for speeding the rate of its convergence, a monotone nonincreasing stepsize rule, and a viscosity approximation method which guaranteed its strong convergence. More so, a strong convergence theorem is proved for the sequence generated by the algorithm under some mild conditions and without prior knowledge of the Lipschitz-like constants of the equilibrium bifunction. We further provide some numerical examples to illustrate the performance and accuracy of our method.

Original languageEnglish
Article number9
JournalFixed Point Theory and Applications
Volume2020
Issue number1
DOIs
Publication statusPublished - 1 Dec 2020

Keywords

  • Common fixed point
  • Equilibrium problems
  • Extragradient method
  • Pseudomonotone
  • Self-adaptive method

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