Applications of Mathematics

, Volume 58, Issue 3, pp 269–278

An intersection theorem for set-valued mappings

Authors

    • Department of MathematicsTexas A&M University
  • Mircea Balaj
    • Department of MathematicsUniversity of Oradea
  • Donal O’Regan
    • Department of MathematicsNational University of Ireland
Article

DOI: 10.1007/s10492-013-0013-7

Cite this article as:
Agarwal, R.P., Balaj, M. & O’Regan, D. Appl Math (2013) 58: 269. doi:10.1007/s10492-013-0013-7
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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: 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.

Keywords

intersection theoremfixed pointsaddle pointequilibrium problemcomplementarity problem

MSC 2010

47H1049J53

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013