Iterative methods for a system of split feasibility problems and fixed point problems in Banach spaces

Abstract

     In this paper, we consider a system of split feasibility problems and fixed point problems in Banach space. By using a shrinking projective method and the modified proximal point algorithm, we propose an iterative algorithm. Under suitable conditions some strong convergence theorems are proved. Our results extend and improve the main result of Takahashi-Xu-Yao (Set-Valued Var. Anal. 23, 205-221 (2015)).