Iterative Algorithm For Systems Of Generalized Implicit Quasi-Variational-Like Inclusions And Of Variational Inclusions With (A, η)-Accretive Mappings

In this paper, we study systems of variational inclusions in purpose. We study iterative algorithm for a new system of generalized implicit quasi-variational-like inclusions and of nonlinear variational inclusions with (A,η)-accretive mappings. We propose some new algorithms for solving these systems of variational inclusions, and prove the sequences of our algorithms for approximating the solutions of these problems. Our results presented in this paper extend and improve many known results in the literatures.In the first chaper, we simply introduce the background and development of systems of variational inclusions and (A,η)-accretive mappings.In the second chaper, we introduce some definitions, knowledge ofη-subdifferentiable mapping andη-proximal mapping. We introduce a new system of generalized implicit quasi-variational-like inclusion problems (GIQVLIP) involvingη-subdifferentiable mapping in Hilbert space. By applying some lemmas, we develop one newη-proximal point algorithm of Mann and Ishikawa type for approximating the unique solution of the system of generalized implicit quasi-variational-like inclusion problems.In the third chaper, we introduce some definitions, and knowledge of (A,η)-accretive mappings. We introduce a new system of nonlinear variational inclusions with (A,η)-accretive mappings in q-uniformly smooth Banach space. By applying the resolvent operator technique associated with the (A,η)-accretive mappings, we prove the existence and uniqueness of the solution of the system of the nonlinear variational inclusions, propose a Mann-type iterative algorithm for approximating the solution and discuss the convergence and stability of the algorithm.