JournalszaaVol. 25 , No. 2DOI 10.4171/zaa/1288

An Existence Result for a Class of Extended Inclusion Problems with Applications to Equilibrium Problems

  • Nan-jing Huang

    Sichuan University, China
  • Ya-ping Fang

    Sichuan University, China
An Existence Result for a Class of Extended Inclusion Problems with Applications to Equilibrium Problems cover

Abstract

Let XX be a real reflexive Banach space, KXK\subset X a nonempty, closed and convex set, and F:K×K2XF:K\times K\to 2^X (the family of all the subsets of XX) be a multi-valued mapping. In this paper, we consider the following extended inclusion problem: find xKx^*\in K such that KF(x,x)K\subset F(x^*,x^*). Under suitable conditions, we establish an existence result for the extended inclusion problem. As applications, we give some existence theorems for equilibrium problems.