In this paper, we introduce a Yosida inclusion problem as well as a generalized Yosida approximation operator. Using the graph convergence of HðÁ; ÁÞ-accretive operator and resolvent operator convergence discussed in Li and Huang (Appl Math Comput 217:9053-9061, 2011), we establish the convergence for generalized Yosida approximation operator. As an application, we solve a Yosida inclusion problem in q-uniformly smooth Banach spaces. An example is constructed, and through MATLAB programming, we show some graphics for the convergence of generalized Yosida approximation operator.
In this paper, we study a Yosida variational inclusion problem with its corresponding Yosida resolvent equation problem. We mention some schemes to solve both the problems, but we focus our study on discussing convergence criteria for the Yosida variational inclusion problem in real Banach space and for the Yosida resolvent equation problem in q-uniformly smooth Banach space. For faster convergence, we apply an inertial extrapolation scheme for both the problems. An example is provided.
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