Applied Set-Valued Analysis and Optimization

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DOI: 10.23952/asvao.6.2024.3.06
Volume 6, Issue 3, 1 December 2024, Pages 319-331

 

Abstract. The purpose of this paper is to investigate the existence of solutions of set-valued quasi-equilibrium problems in real Banach spaces. We introduce a concept of Brezis pseudomonotonicity for set-valued mappings. By constructing appropriate constraint conditions for the weak coercive function and the objective mapping, we obtain a solution-existence result for usual set-valued equilibrium problems. By a sequence of penalized set-valued equilibrium problems, we obtain a solution-existence result for set-valued quasi-equilibrium problems. These results do not require the assumption of compactness of the constraint set, and improve the corresponding ones in the literature.

 

How to Cite this Article:
H. Huang, S. Ge, Penalty method for set-valued quasi-equilibrium problems, Appl. Set-Valued Anal. Optim. 6 (2024), 319-331.