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Displaying similar documents to “On some Optimization Problems in Not Necessarily Locally Convex Space”

An intersection theorem for set-valued mappings

Ravi P. Agarwal, Mircea Balaj, Donal O'Regan (2013)

Applications of Mathematics

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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. ...