Graph Convergence and Approximation Solvability of a Class of Implicit Variational Inclusion Problems in Banach Spaces

This paper deals with a general class of nonlinear implicit variational inclusion problems in 2-uniformly smooth Banach spaces. Applying the generalized resolvent operator technique involving A-maximal m-relaxed monotonicity, the existence and uniqueness solution of the proposed problem is established. Using the generalized graph convergence, an implicit algorithm is developed that approximates the unique solution. Finally, the convergence analysis of the proposed algorithm is accomplished. Similar results are also explored for other classes of maximal monotone mappings.