Strong convergence inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems

Lateef Olakunle Jolaoso*, Maggie Aphane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseudocontractive mapping in real Hilbert spaces. The self-adaptive technique ensures the convergence of the algorithm without any prior estimate of the Lipschitz constant. With the aid of Moudafi’s viscosity approximation method, we prove a strong convergence result for the sequence generated by our algorithm under some mild conditions. We also provide some numerical examples to illustrate the accuracy and efficiency of the algorithm by comparing with other recent methods in the literature.

Original languageEnglish
Article number261
JournalJournal of Inequalities and Applications
Volume2020
Issue number1
DOIs
Publication statusPublished - 2020

Keywords

  • Extragradient method
  • Fixed point
  • Pseudomonotone
  • Self-adaptive stepsize
  • Strong convergence
  • Variational inequalities

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