Convergence analysis of new over-relaxed proximal point algorithm frameworks with errors and applications to general A-monotone nonlinear inclusion forms

摘要

The purpose of this paper is to introduce and study a new class of over-relaxed proximal point algorithm frameworks with errors based on general A-monotonicity. Further, by using Alber’s inequalities, the definition of normalized duality mapping on the dual spaces of Banach spaces and the new proximal mapping technique associated with the general A-monotone operators, we discuss the approximation solvability of general A-monotone nonlinear inclusion forms in Banach spaces and prove the convergence analysis of iterative sequences generated by the algorithm frameworks via applying the Lipschitz continuity of (that is, the inverse of multi-valued operator M) and the Lipschitz continuity of proximal mapping associated with the general A-monotone operators, respectively. Finally, some applications are given to show that the results presented in this paper improve, generalize and unify the corresponding results of recent works.