期刊
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
卷 170, 期 2, 页码 629-649出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-015-0854-1
关键词
Quasi-equilibrium problem; Set-valued mapping; Semicontinuity; Fixed point; Continuous selection
This paper deals with quasi-equilibrium problems in the setting of real Banach spaces. By a fixed point theory approach, we obtain existence results under mild conditions of continuity, improving some previous results in this area. By a selection theory approach, we make use of the Michael selection theorem to overcome the separability of the Banach spaces and generalize some results obtained recently in the literature. Finally, we deal with the existence of approximate solutions for quasi-equilibrium problems, and by arguments combining selection theory and fixed point theory, we obtain some qualitative results for quasi-equilibrium problems involving sub-lower semicontinuous set-valued mappings.
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