New strong convergence analysis for variational inequalities and fixed point problems

Izuchukwu C., Shehu Y., Yao J.

Optimization, vol.75, no.2, pp.413-434, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 75 Issue: 2
  • Publication Date: 2026
  • Doi Number: 10.1080/02331934.2024.2424446
  • Journal Name: Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Page Numbers: pp.413-434
  • Keywords: Forward-backward-forward method, Hilbert spaces, krasnoselskii–Mann, strong convergence, variational inequality and fixed point problem
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this paper, we obtain strong convergence results for solving variational inequality and fixed point problems using a combination of the Forward-Backward-Forward method and the Krasnoselkii–Mann iteration method with an inertial extrapolation step without assuming on-line rule of the inertial parameters and the iterates. Our results present a new way of choosing inertial parameters for strongly convergent algorithms to solve variational inequality and fixed point problems different from what is obtainable in the literature whereby on-line rule is assumed. We perform numerical tests to validate our theoretical analysis.