Contributions to the convergence analysis of nonconvex equilibrium problems

Messaoud Bounkhel; Messaoud Bounkhel

doi:10.3934/math.2025954

AIMS Mathematics

2025, Volume 10, Issue 9: 21468-21491. doi: 10.3934/math.2025954

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Research article

Contributions to the convergence analysis of nonconvex equilibrium problems

Messaoud Bounkhel ^,

Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 26 May 2025 Revised: 27 August 2025 Accepted: 05 September 2025 Published: 17 September 2025
MSC : 34A60, 49J53

This paper establishes a successive approximation method designed to compute a point belonging simultaneously to the fixed-point set of a given mapping (relatively nonexpansive) and to the solution set of a nonconvex equilibrium problem within a Banach space. Our present findings provide a unifying generalization of numerous previously obtained results, beginning with the transition from Hilbertian structures to the more general Banach framework, and further encompassing the passage from convex analytical settings to their considerably more delicate nonconvex counterparts. We mainly extend the results proved in ^[27] from convex to nonconvex settings.
Citation: Messaoud Bounkhel. Contributions to the convergence analysis of nonconvex equilibrium problems[J]. AIMS Mathematics, 2025, 10(9): 21468-21491. doi: 10.3934/math.2025954

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Abstract

This paper establishes a successive approximation method designed to compute a point belonging simultaneously to the fixed-point set of a given mapping (relatively nonexpansive) and to the solution set of a nonconvex equilibrium problem within a Banach space. Our present findings provide a unifying generalization of numerous previously obtained results, beginning with the transition from Hilbertian structures to the more general Banach framework, and further encompassing the passage from convex analytical settings to their considerably more delicate nonconvex counterparts. We mainly extend the results proved in ^[27] from convex to nonconvex settings.

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