A modified extra-gradient method for a family of strongly pseudomonotone equilibrium problems in real hilbert spaces

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Rehman H. U., Pakkaranang N., Hussain A., Wairojjana N.

Journal of Mathematics and Computer Science, vol.22, no.1, pp.38-48, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.22436/jmcs.022.01.04
  • Journal Name: Journal of Mathematics and Computer Science
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.38-48
  • Keywords: Equilibrium problem, Lipschitz-type conditions, Strong convergence theorem, Strongly pseudomonotone bifunction, Variational inequality problems
  • Uşak University Affiliated: No

Abstract

In this paper, we propose a modified extragradient method for solving a strongly pseudomonotone equilibrium problem in a real Hilbert space. A strong convergence theorem relative to our proposed method is proved and the proposed method has worked without having the information of a strongly pseudomonotone constant and the Lipschitz-type constants of a bifunction. We have carried out our numerical explanations to justify our well-established convergence results, and we can see that our proposed method has a substantial improvement over the time of execution and number iterations.