A System Of Completely Generalized Strongly Quasi-variational Inclusions In Banach Spaces

In this paper, a new system of completely generalized strongly quasi-variational inclusions and concept of J - proximal mapping for a subdifferentiable proper functional are introduced and studied in Banach spaces. The existence and Lipschitz continuity of the J -proximal mapping are proved. Existence of solutions for the system of completely generalized strongly quasi-variational inclusions involving expanding and strongly accretive mappings is obtained, respectively. By employing the J -proximalmapping, several differential iterative algorithms for approximating the solutions are constructed and convergence of the iterative sequences generated by these algorithms are gained. The behavior and sensitivity analysis of solutions for a class of system of generalized variational inequalities are also studied in Hilbert space. Numerical related results are improved, extended and unified.