Applications of Mathematics

, Volume 58, Issue 3, pp 269-278

First online:

An intersection theorem for set-valued mappings

  • Ravi P. AgarwalAffiliated withDepartment of Mathematics, Texas A&M University Email author 
  • , Mircea BalajAffiliated withDepartment of Mathematics, University of Oradea
  • , Donal O’ReganAffiliated withDepartment of Mathematics, National University of Ireland

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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: XX, S: YX we prove that under suitable conditions one can find an xX 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.


intersection theorem fixed point saddle point equilibrium problem complementarity problem

MSC 2010

47H10 49J53