By introducing a concept called ’couple-majorized mapping’ in product topoogical vector spaces we establish existence theorems of maximal elements for couple.majorized set-valued families with arbitrary index set. As applications, some component coincidence and fixed points theorems are given which could be regarded as product extension version of the Fan-Browder fixed point theorem and related coincidence theorems. Finally, a coincidence theorem is used to derive the Sion minimax inequality in the case of two functions.
Cite this article
P. Deguire, Xian-Zhi Yuan, Maximal Elements and Coincident Points for Couple-Majorized Mappings in Product Topological Vector Spaces. Z. Anal. Anwend. 14 (1995), no. 4, pp. 665–676