An intersection theorem for set-valued mappings
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- Agarwal, R.P., Balaj, M. & O’Regan, D. Appl Math (2013) 58: 269. doi:10.1007/s10492-013-0013-7
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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.