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Journal of Convex Analysis 24 (2017), No. 3, 1015--1028
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 - Meguro-ku, Tokyo 152-8552, Japan

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 well-known 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

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