JournalszaaVol. 25, No. 2pp. 257–264

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
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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.

Cite this article

Nan-jing Huang, Ya-ping Fang, An Existence Result for a Class of Extended Inclusion Problems with Applications to Equilibrium Problems. Z. Anal. Anwend. 25 (2006), no. 2, pp. 257–264

DOI 10.4171/ZAA/1288