Existence and Iterative Approximations of Solution for Generalized Yosida Approximation Operator

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and generalized Yosida approximation operator. We also furnish an illustrative example to demonstrate our results. Furthermore, we suggest an iterative algorithm to solve a Yosida inclusion problem under some mild conditions in q-uniformly smooth Banach space and discuss the convergence and uniqueness of the solution.