Generalized Eckstein–Bertsekas proximal point algorithm involving -monotonicity framework

A general framework for the Eckstein–Bertsekas proximal point algorithm, based on the notion of ( 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 ) -monotonicity are given.