Work

Existence of projected solutions for a quasi-equilibrium problem with applications

Year: 2026

Type: article

Abstract: This article studies a quasi-equilibrium problem (QEP, for short) in an infinite dimensional Banach space $X$. Under very mild assumptions, we establish nonemptiness and compactness of projected solution set to (QEP), both in the cases when $X$ is reflexive or not.The main strategy is based on the Michael selection theorem, the Schauder fixed-point theorem, an approximating technique and the concept of approximatively compactness. As application of the obtained results, we focus on three problems with non-self and implicit constraints which are, respectively, a quasi-variational-hemivariational inequality, a quasi-optimization problem, and a generalized Nash equilibrium problem.

Source: Hacettepe Journal of Mathematics and Statistics

DOI: 10.15672/hujms.1802593

Authors: Yunyun Wu, Xi Chen, Calogero Vetro, Xiuwen Li

Institutions: Guizhou University, University of Palermo, Guangxi Minzu University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Università degli Studi di Palermo

Awards: G6204808264, G748098572