A class of Yosida inclusion and graph convergence on Yosida approximation mapping with an application

Abstract

The proposed work is presented in two folds. The first aim is to deals with the new notion called generalized ?i?j-Hp(., ., ...)-accretive mappings that are the sum of two symmetric accretive mappings. It is an extension of ??-H(., .)-accretive mapping, studied and analyzed by Kazmi [18]. We define the proximalpoint mapping associated with generalized ?i?j-Hp(., ., ...)-accretive mapping and demonstrate aspects on single-valued property and Lipschitz continuity. The graph convergence of generalized ?i?j-Hp(., ., ...)- accretive mapping is discussed. Second aim is to introduce and study the generalized Yosida approximation mapping and Yosida inclusion problem. Next, we obtain the convergence on generalized Yosida approximation mappings by using the graph convergence of generalized ?i?j-Hp(., ., ...)-accretive mappings without using the convergence of its proximal-point mapping. As an application, we consider the Yosida inclusion problem in q-uniformly smooth Banach spaces and propose an iterative scheme connected with generalized Yosida approximation mapping of generalized ?i?j-Hp(., ., ...)-accretive mapping to find a solution of Yosida inclusion problem and discuss its convergence criteria under appropriate assumptions. Some examples are constructed and demonstrate few graphics for the convergence of proximal-point mapping as well as generalized Yosida approximation mapping linked with generalized ?i?j-Hp(., ., ...)-accretive mappings.