An intersection theorem for set-valued mappings |
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Authors: | Ravi P Agarwal Mircea Balaj Donal O’Regan |
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Institution: | 1. Department of Mathematics, Texas A&M University, Kingsville, TX, 78363, USA 2. Department of Mathematics, University of Oradea, Oradea, Romania 3. Department of Mathematics, National University of Ireland, Galway, Ireland
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Abstract: | 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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