The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (120 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 25, Issue 2, 2006, pp. 257–264
DOI: 10.4171/ZAA/1288

Published online: 2006-06-30

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

Ya-ping Fang[1] and Nan-jing Huang[2]

(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