Strong convergence of a self-adaptive method for the split feasibility problem in Banach spaces

Abstract

© 2018, Springer International Publishing AG, part of Springer Nature. In signal processing and image reconstruction, the split feasibility problem (SFP) has been now investigated extensively because of its applications. A classical way to solve the SFP is to use Byrne’s CQ-algorithm. However, this method requires the computation of the norm of the bounded linear operator or the matrix norm in a finite-dimensional space. In this work, we aim to propose an iterative scheme for solving the SFP in the framework of Banach spaces. We also introduce a new way to select the step-size which ensures the convergence of the sequences generated by our scheme. We finally provide examples including its numerical experiments to illustrate the convergence behavior. The main results are new and complements many recent results in the literature.