Modified inertial viscosity extrapolation method for solving quasi-monotone variational inequality and fixed point problems in real Hilbert spaces

Jacob A. Abuchu, Austine E. Ofem, Hüseyin Işık*, Godwin C. Ugwunnadi, Ojen K. Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce and study a viscous-type extrapolation algorithm for finding a solution of the variational inequality problem and a fixed point constraint of quasi-nonexpansive mappings under the scope of real Hilbert spaces when the underlying cost operator is quasi-monotone. The method involves inertial viscosity approximation and a constructed self-adjustable step size condition that depends solely on the information of the previous step. We establish a strong convergence result of the proposed method under certain mild conditions on the algorithm parameters. Finally, to demonstrate the gain of our method, some numerical examples are presented in comparison with some related methods in literature.

Original languageEnglish
Article number38
JournalJournal of Inequalities and Applications
Volume2024
Issue number1
DOIs
Publication statusPublished - Jan 2024
Externally publishedYes

Keywords

  • 47H05
  • 47J20
  • 47J25
  • 65K15
  • Inertial extrapolation method
  • Quasi-monotone operator
  • Strong convergence
  • Variational inequality
  • Viscosity approximation

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