
Journal of Convex Analysis 24 (2017), No. 3, 10151028 Copyright Heldermann Verlag 2017 The Split Common Fixed Point Problem and the Shrinking Projection Method in Banach Spaces Wataru Takahashi Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80702, Taiwan and: Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama  Meguroku, Tokyo 1528552, Japan wataru@is.titech.ac.jp We consider the split common fixed point problem in Banach spaces. Using the shrinking projection method, we prove a strong convergence theorem for finding a solution of the common fixed point problem in Banach spaces. Using this result, we get wellknown and new results which are connected with the split feasibility problem and the split common null point problem in Banach spaces. Keywords: Split common fixed point problem, fixed point, metric projection, metric resolvent, shrinking projection method, duality mapping. MSC: 47H05, 47H09 [ Fulltextpdf (134 KB)] for subscribers only. 