Generalized over-relaxed proximal algorithm based on A-maximal monotonicity framework and applications to inclusion problems

General framework for the over-relaxed proximal point algorithm using the notion of A -maximal monotonicity (also referred to as A -monotonicity in the literature) is developed, and then the convergence analysis for this algorithm in the context of solving a general class of nonlinear inclusion problems is examined along with some auxiliary results involving A -maximal monotone mappings in a Hilbert space setting.