Journal of Convex Analysis 27 (2020), No. 2, 623--644
Copyright Heldermann Verlag 2020
The Split Common Fixed Point Problem by the Hybrid Method for Families of New Demimetric Mappings in Banach Spaces
Wataru Takahashi
Center for Fundamental Science, Research Center for Nonlinear Analysis, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
and: Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Tokyo 152-8552, Japan
wataru@is.titech.ac.jp
Ching-Feng Wen
Center for Fundamental Science, Research Center for Nonlinear Analysis, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
cfwen@kmu.edu.tw
Jen-Chih Yao
Center for General Education, China Medical University, Taichung 40402, Taiwan
yaojc@mail.cmu.edu.tw
We consider the split common fixed point problem for families of mappings in Banach spaces. Using the hybrid method, we prove two strong convergence theorems of finding a solution of the split common fixed point problem for families of generalized demimetric mappings in Banach spaces. We also apply these results to obtain well-known and new results for the split common fixed point problem in Banach spaces.
Keywords: Split common fixed point problem, metric projection, metric resolvent, generalized demi-metric mapping, hybrid method.
MSC: 47H05, 47H09
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