Graph Convergence, Algorithms, and Approximation of Common Solutions of a System of Generalized Variational Inclusions and Fixed-Point Problems

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in proximal mapping associated with a general H-monotone operator, its Lipschitz continuity is proved an estimate of constant computed. The main contribution work establishment equivalence relationship between graph convergence sequence strongly their mappings, respectively, to given by using notions concerning mapping. By employing concept relating mapping, iterative algorithms are proposed, as application obtained mentioned above, theorem for approximating common element set solutions system generalized variational inclusions involving fixed points ({an},{bn},ϕ)-total uniformly L-Lipschitzian proved. It significant emphasize that our results improve generalize many known corresponding results.