Algorithms of solutions for completely generalized mixed implicit quasi-variational inclusions

摘要

In this paper, by applying resolvent operator technique, an existence theorem of solutions for a class of completely generalized mixed implicit quasi-variational inclusions involving relaxed Lipschitz, generalized pseudo-contractive and relaxed monotone 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.