An intersection theorem for set-valued mappings

被引：0
作者：
Ravi P. Agarwal
Mircea Balaj
Donal O’Regan
机构：
[1] Texas A&M University,Department of Mathematics
[2] University of Oradea,Department of Mathematics
[3] National University of Ireland,Department of Mathematics
来源：
Applications of Mathematics | 2013年 / 58卷
关键词：
intersection theorem; fixed point; saddle point; equilibrium problem; complementarity problem; 47H10; 49J53;
D O I：
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中图分类号：
学科分类号：
摘要：
Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T: X ⇉ X, S: Y ⇉ X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S. Applying our intersection theorem, we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.
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页码：269 / 278
页数：9
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