Rockafellar\u27S Celebrated Theorem Based On A -Maximal Monotonicity Design

A generalization to Rockafellar\u27s theorem (1976) in the context of approximating a solution to a general inclusion problem involving a set-valued A-maximal monotone mapping using the proximal point algorithm in a Hilbert space setting is presented. Although there exists a vast literature on this theorem, most of the studies are focused on just relaxing the proximal point algorithm and applying to the inclusion problems. The general framework for A-maximal monotonicity (also referred to as the A-monotonicity framework in literature) generalizes the general theory of set-valued maximal monotone mappings, including the H-maximal monotonicity (also referred to as H-monotonicity). © 2007 Elsevier Ltd. All rights reserved