Nonempty Intersection Theorems and Generalized Multi-objective Games in Product FC-Spaces

  • Authors:

  • Xie Ping Ding

  • Affiliations:

  • College of Mathematics and Software Science, Sichuan Normal University, Chengdu, P. R. China 610066

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2007

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Abstract

A new class of generalized multi-objective games is introduced and studied in FC-spaces where the number of players may be finite or infinite, and all payoff are all set-valued mappings and get their values in a topological space. By using an existence theorems of maximal elements for a family of set-valued mappings in product FC-spaces due to author, some new nonempty intersection theorems for a family of set-valued mappings are first proved in FC-spaces. As applications, some existence theorems of weak Pareto equilibria for the generalized multi-objective games are established in noncompact FC-spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.