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 theorem fixed point saddle point equilibrium problem complementarity problem 

MSC 2010

47H10 49J53 

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

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