A cyclic iterative method for solving multiple sets split feasibility problems in Banach spaces

Abstract

In this paper, we construct an iterative scheme and prove strong convergence theorem of the sequence generated to an approximate solution to a multiple sets split feasibility problem in a p-uniformly convex and uniformly smooth real Banach space. Some numerical experiments are given to study the efficiency and implementation of our iteration method. Our result complements the results of F. Wang (A new algorithm for solving the multiple-sets split feasibility problem in Banach spaces, Numerical Functional Anal. Optim. 35 (2014), 99{110), F. Schöpfer et al. (An iterative regularization method for the solution of the split feasibility problem in Banach spaces, Inverse Problems 24 (2008), 055008) and many important recent results in this direction.

Mathematics Subject Classification (2010): 49J53, 65K10, 49M37, 90C25.

Keywords: Bregman projection, strong convergence, metric projection, split feasibility problem, uniformly convex, uniformly smooth