On Solving the Split Feasibility Problem and the Fixed Point Problem in Banach Spaces

Prasit Choalmjiak, Pongsakorn Sunthrayuth

Abstract

In this paper, we introduce an iterative method for solving the splitfeasibility problem and the fixed point problem of countable family of Bregman relatively nonexpansive mappings in the framework of p-uniformly convex anduniformly smooth Banach spaces. Then, we prove strong convergence theoremof the sequence generated by our iterative scheme with a new way of selectingthe step-size which does not require the computation on the norm of the boundedlinear operator. The obtained result of this paper complements many recent resultsin this direction.