%0 Journal Article
%T Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces
%A Lu-Chuan Ceng
%A Ching-Feng Wen
%J Journal of Applied Mathematics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/194509
%X We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations of the corresponding inclusion problem and corresponding fixed point problem. Furthermore, we derive some conditions under which the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the existence and uniqueness of its solution.
%U http://www.hindawi.com/journals/jam/2012/194509/