A Generalized Proximal Point Algorithm and Implicit Iterative Schemes for a Sequence of Operators on Banach Spaces

The aim of this paper is to obtain weak convergence of an iterative scheme generated by a sequence of accretive operators defined on a real Banach space, which is a generalization of the result given by Kamimura and Takahashi (J. Approx. Theory 106:226–240, 2000). We also show several applications to the implicit iterative schemes with the Yosida approximations and with the W-mappings generated by a sequence of nonexpansive mappings.