Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Split common fixed point problem
  • metric projection
  • metric resolvent
  • generalized demi-metric mapping
  • hybrid method

Mathematics Subject Classification

47H05, 47H09

Suggested citation

W. Takahashi, C.-F. Wen, J.-C. Yao. “The Split Common Fixed Point Problem by the Hybrid Method for Families of New Demimetric Mappings in Banach Spaces.” Journal of Convex Analysis 27 (2020), No. 2, 623–644.

Copyright Heldermann Verlag 2020