On the weak and strong convergence of the proximal point algorithm in reflexive Banach spaces

Abstract

In this paper, some proximal point algorithms (PPAs) for maximal monotone operators in Banach spaces are considered. We obtain some results on the boundedness and the convergence of sequences generated by the PPAs with some assumptions. We can also get zero of maximal -expansive operator and maximal -monotone at zero operator using this method and then we apply it for finding a solution of the equilibrium problem.