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In this paper, we introduce a Yosida inclusion problem as well as a generalized Yosida approximation operator. Using the graph convergence of $$H(\cdot ,\cdot )$$ -accretive operator and resolvent operator convergence discussed in Li and Huang (Appl Math Comput 217:9053-9061, 7), 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. [ABSTRACT FROM AUTHOR]