ISAS - Recent advances in applied sciences
Convergence of the solutions for weak vector quasi-equilibrium problems
- Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), Vietnam National University (VNU-HCM), Ho Chi Minh City, Vietnam
- Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Ho Chi Minh City, Vietnam
Correspondence to:
Xuan Dai Le,
Department of Applied Mathematics, Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), Vietnam National University (VNU-HCM), Ho Chi Minh City, Vietnam.
Email:
[email protected].
Published:
2026-09-23
Abstract
In this paper, we first establish weak vector quasi-equilibrium problems in finite dimensional spaces. After that, we introduce the auxiliary solution sets and the concept of quasi-convexity of the objective functions for weak vector quasi-equilibrium problems. Finally, based on the auxiliary solution sets and the concept of quasi-convexity, we study the Painlevé-Kuratowski lower convergence and convergence of the solution sets with a sequence of mappings converging continuously for these problems. Many examples are given for the illustration of our results. Our results in this paper are new and different some main results in the literature.
Keywords:
Weak quasi-equilibrim problems
Painlevé- Kuratowski upper (lower) convergence
Painlevé- Kuratowski convergence