Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2006-06-30
An Existence Result for a Class of Extended Inclusion Problems with Applications to Equilibrium ProblemsYa-ping Fang and Nan-jing Huang (1) Sichuan University, China
(2) Sichuan University, China
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.
Keywords: Extended inclusion problem, equilibrium problem, variational inequality, existence
Fang Ya-ping, Huang Nan-jing: An Existence Result for a Class of Extended Inclusion Problems with Applications to Equilibrium Problems. Z. Anal. Anwend. 25 (2006), 257-264. doi: 10.4171/ZAA/1288