Iterative methods for solving split feasibility problems and fixed point problems in Banach spaces

Abstract

In this paper, we consider
a class of split feasibility problems in Banach space. By using
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 a
recent result of Takahashi-Xu-Yao (Set-Valued
Var. Anal. 23, 205-221 (2015)) from Hilbert spaces to Banach spaces. Moreover, the method
of proof is also different.