EXISTENCE AND ALGORITHM OF SOLUTIONS FOR GENERALIZED MIXED IMPLICIT QUASIVARIATIONAL INEQUALITIES

Abstract

In this paper, by applying a new projecting operator technique, an existence theorem of solutions for a class of generalized mixed implicit quasi-variational inequalities involving relaxed Lipschitz and pseudocontractive set-valued mappings is proved in Hilbert spaces. A novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed. The convergence criteria is also given. These results of existence, algorithm and convergence are new, and unify and generalize some corresponding results in recent literatures.