# 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

## Abstract

Let $X$ be a real reflexive Banach space, $K\subset X$ a nonempty, closed and convex set, and $F:K\times K\to 2^X$ (the family of all the subsets of $X$) be a multi-valued mapping. In this paper, we consider the following extended inclusion problem: find $x^*\in K$ such that $K\subset F(x^*,x^*)$. 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