Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1995-12-31
Maximal Elements and Coincident Points for Couple-Majorized Mappings in Product Topological Vector SpacesP. Deguire and Xian-Zhi Yuan (1) University of Moncton, Canada
(2) The University of Queensland, Brisbane, Australia
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.
Keywords: Couple-majorized mappings, Fan-Browder fixed point theorem, maximal elements, coincidence points, minimaz inequalities, Knaster-Kuratowski-Mazurkiewicz lemma and product spaces
Deguire P., Yuan Xian-Zhi: Maximal Elements and Coincident Points for Couple-Majorized Mappings in Product Topological Vector Spaces. Z. Anal. Anwend. 14 (1995), 665-676. doi: 10.4171/ZAA/646