Journal of Global Optimization

, Volume 57, Issue 4, pp 1359–1373 | Cite as

Minimax theorems for scalar set-valued mappings with nonconvex domains and applications

  • Y. Zhang
  • S. J. Li


In this paper, by virtue of the separation theorem of convex sets, we prove a minimax theorem, a cone saddle point theorem and a Ky Fan minimax theorem for a scalar set-valued mapping under nonconvex assumptions of its domains, respectively. As applications, we obtain an existence result for the generalized vector equilibrium problem with a set-valued mapping. Simultaneously, we also obtain some generalized Ky Fan minimax theorems for set-valued mappings, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization.


Minimax theorem Cone saddle point Vector optimization Set-valued mapping 

Mathematics Subject Classification (2010)

49J35 49K35 90C47 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsChongqing UniversityChongqingChina

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