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
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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