A Class of a System of Multi-Valued Extended General Quasi-Variational Inequality Problems

Saleh A. Al-Mezel, Faizan A. Khan

Abstract

In this paper, we consider a system of multi-valued extended general quasi-variational inequality problems (SMEGQVIP) in real Hilbert spaces. Using the projection operator technique, it is observed that the SMEGQVIP is equivalent to the system of projection equations. This alternative equivalence formulation is used to suggest an iterative algorithm for the SMEGQVIP. Further, we prove the existence of a solution of SMEGQVIP and discuss the convergence analysis of iterative sequences generated by given algorithm. The approach used in this paper may be treated as an extension and unification of approaches for studying existence results for various important classes of system of variational inequality problems given by many authors in this direction.