International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 21, Pages 3373-3385
doi:10.1155/IJMMS.2005.3373
Generalized g-quasivariational inequality
1ISTIT-LOSI (CNRS FRE 2732), Technology University of Troyes, 12 Rue Marie Curie, BP 2060, Troyes Cedex 10010, France
2Department of Business Administration, Faculty of Economics andManagement Sciences, International Islamic University Malaysia (IIUM), Jalan Gombak, Kuala Lumpur 53100, Malaysia
Received 25 May 2005; Revised 7 October 2005
Copyright © 2005 Rabia Nessah and Moussa Larbani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Suppose that X is a nonempty subset of a metric space E and Y is a nonempty subset of a topological vector space F. Let g:X→Y and ψ:X×Y→ℝ be two functions and let S:X→2Y and T:Y→2F∗ be two maps. Then the generalized g-quasivariational inequality problem (GgQVI) is to find a point x¯∈X and a point f∈T(g(x¯)) such that g(x¯)∈S(x¯) and supy∈S(x¯){Re〈f,y−g(x¯)〉+ψ(x¯,y)}=ψ(x¯,g(x¯)). In this paper, we prove the existence of a solution of (GgQVI).