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In this paper, we introduce and study a new class of over-relaxed (A,η,m)-proximal point iterative methods with errors for solving general nonlinear operator equations in Hilbert spaces. By using Liu’s inequality and the generalized resolvent operator technique associated with (A,η,m)-monotone operators, we also prove the existence of solution for the nonlinear operator inclusions and discuss the graph-convergent analysis of iterative sequences generated by the algorithm. Furthermore, we give some examples and an application for solving the open question (2) due to Li and Lan (Adv. Nonlinear Var. Inequal. 15(1):99-109, 2012). The numerical simulation examples are given to illustrate the validity of our results.

Graph-convergent analysis of over-relaxed ( A , η , m ) -proximal point iterative methods with errors for general nonlinear operator equations