An intersection theorem in L-convex spaces with applications

• Published in: Journal of mathematical analysis and applications Vol. 312; no. 1; pp. 343 - 356
• Main Authors: Lu, Haishu, Tang, Deshan
• Format: Journal Article
• Language: English
• 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

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...