An iterative method for solving multiple-set split feasibility problems in Banach spaces

Abstract

"In this paper, we study generalized multiple-set split feasibility problems (in short, GMSSFP) in the frame workof p-uniformly convex real Banach spaces which are also uniformly smooth. We construct an iterative algo-rithm which is free from an operator norm and prove its strong convergence to a solution of GMSSFP, thatis, a solution of convex problem and a common fixed point of a countable family of Bregman asymptoticallyquasi-nonexpansive mappings without requirement for semi-compactness on the mappings. We illustrate ouralgorithm and convergence result by a numerical example. "