PROXIMAL POINT ALGORITHMS BASED ON THE (A, 𝜂)-MONOTONE MAPPINGS

In this paper, we consider proximal point algorithms based on ($A,{\eta}$)-monotone mappings in the framework of Hilbert spaces. Since ($A,{\eta}$)-monotone mappings generalize A-monotone mappings, H-monotone mappings and many other mappings, our results improve and extend the recent ones announced by [R.U. Verma, Rockafellars celebrated theorem based on A-maximal monotonicity design, Appl. Math. Lett. 21 (2008), 355-360] and [ R.T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim. 14 (1976) 877-898] and some others.