Generalized Eckstein–Bertsekas proximal point algorithm involving (H,η)(H,η)-monotonicity framework

A general framework for the Eckstein–Bertsekas proximal point algorithm, based on the notion of (H,η)(H,η)-monotonicity, is developed. Convergence analysis for the generalized Eckstein–Bertsekas proximal point algorithm in the context of solving a class of nonlinear inclusions is examined. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to (H,η)(H,η)-monotonicity are given.