Existence and approximation of solutions for generalized extended nonlinear variational inequalities

摘要

In this paper, we consider a new class of generalized extended nonlinear quasi-variational inequality problems involving set-valued relaxed monotone operators and establish its equivalence with the fixed point problem. We study criteria for existence of their solutions. Iterative methods for finding approximate solutions are also proposed and analyzed. MSC:47J20, 65K10, 65K15, 90C33.