An intersection theorem in L-convex spaces with applications

A new intersection theorem is obtained in L-convex spaces without linear structure. As its applications, a fixed point theorem, a maximal element theorem, a coincidence theorem, some new minimax inequalities and a saddle point theorem are given in L-convex spaces. Our results generalize many known t...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 312; no. 1; pp. 343 - 356
Main Authors Lu, Haishu, Tang, Deshan
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.12.2005
Elsevier
Subjects
Coincidence theorem
Exact sciences and technology
Fixed point
Functional analysis
Global analysis, analysis on manifolds
Intersection theorem
L-quasiconcave (quasiconvex)
Mathematical analysis
Mathematics
Maximal element
Minimax inequality
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Transfer compactly closed-valued (open-valued)
Transfer compactly closed-valued (open-valued)
Coincidence theorem
Maximal element
Minimax inequality
L-quasiconcave (quasiconvex)
Intersection theorem
Fixed point
Space application
Saddle point method
Linear structure
Saddle point
Fixed point theorem
Mathematical analysis
Linear space
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Summary:A new intersection theorem is obtained in L-convex spaces without linear structure. As its applications, a fixed point theorem, a maximal element theorem, a coincidence theorem, some new minimax inequalities and a saddle point theorem are given in L-convex spaces. Our results generalize many known theorems in the literature.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2005.03.085