Generalized minimax inequalities for set-valued mappings

S. J. Li, G. Y. Chen, K. L. Teo, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

25 Citations (Scopus)

Abstract

In this paper, we study generalized minimax inequalities in a Hausdorff topological vector space, in which the minimization and the maximization of a two-variable set-valued mapping are alternatively taken in the sense of vector optimization. We establish two types of minimax inequalities by employing a nonlinear scalarization function and its strict monotonicity property. Our results are obtained under weaker convexity assumptions than those existing in the literature. Several examples are given to illustrate our results.
Original languageEnglish
Pages (from-to)707-723
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume281
Issue number2
DOIs
Publication statusPublished - 15 May 2003

Keywords

  • Maximal point
  • Minimal point
  • Minimax inequality
  • Nonlinear scalarization function
  • Set-valued mapping

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this