New strong convergence analysis for variational inequalities and fixed point problems
Optimization, vol.75, no.2, pp.413-434, 2026 (SCI-Expanded, Scopus)
- 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.