Applications of Mathematics

, Volume 58, Issue 3, pp 269–278

An intersection theorem for set-valued mappings


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


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 theoremfixed pointsaddle pointequilibrium problemcomplementarity problem

MSC 2010


Copyright information

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

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
  • Mircea Balaj
    • 2
  • Donal O’Regan
    • 3
  1. 1.Department of MathematicsTexas A&M UniversityKingsvilleUSA
  2. 2.Department of MathematicsUniversity of OradeaOradeaRomania
  3. 3.Department of MathematicsNational University of IrelandGalwayIreland