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

Boualem Alleche () and Vicenţiu D. Rădulescu ()
Additional contact information
Boualem Alleche: Université de Médéa
Vicenţiu D. Rădulescu: King Abdulaziz University

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 2, No 16, 629-649

Abstract: Abstract 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.

Keywords: Quasi-equilibrium problem; Set-valued mapping; Semicontinuity; Fixed point; Continuous selection; 47J20; 49J35; 49J53; 46N10 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-015-0854-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-015-0854-1

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-015-0854-1

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().