Solutions and Approximate Solutions of Quasi-Equilibrium Problems in Banach Spaces

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2016-08, Vol.170 (2), p.629-649
Main Authors: Alleche, Boualem, Rădulescu, Vicenţiu D.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Banach space
Banach spaces
Calculus of Variations and Optimal Control
Optimization
Continuity
Engineering
Equilibrium
Game theory
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Studies
Theorems
Theory of Computation
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-015-0854-1