On the well-posedness of the generalized split quasi-inverse variational inequalities

Abstract

In this paper, a generalized split quasi-inverse variational inequality ((GSQIVI), for short) is considered and investigated in Hilbert spaces. Since the well-posedness results, not only show us the qualitative properties of problem (GSQIVI), but also it gives us an outlook to the convergence analysis of the solutions for (GSQIVI). Therefore, we first introduce the concepts concerning with the approximating sequences, well-posedness and well-posedness in the generalized sense of (GSQIVI). Then, under those definitions, we establish several metric characterizations and equivalent conditions of well-posedness for the (GSQIVI) by using the measure of noncompactness theory and the generalized Cantor theorem. c 2016 All rights reserved.Keywords: Generalized split quasi-inverse variational inequality, measure of noncompactness, well-posedness, Painlevé-Kuratowski limits. 2010 MSC: 49J53, 49K40, 90C33, 90C46.