An intersection theorem for set-valued mappings

Agarwal, Ravi P.
Balaj, Mircea
O’Regan, Donal
Agarwal, Ravi P. Balaj, Mircea; O’Regan, Donal (2013). An intersection theorem for set-valued mappings. Applications of Mathematics 58 (3), 269-278
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 a double dagger parts per thousand X, S: Y a double dagger parts per thousand X we prove that under suitable conditions one can find an x a 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.
Institute of Mathematics, Czech Academy of Sciences
Publisher DOI
Attribution-NonCommercial-NoDerivs 3.0 Ireland