Abstract

We deal with the split common fixed point problem in two Banach spaces. Using the resolvents of maximal monotone operators, demimetric mappings, demigeneralized mappings in Banach spaces, we prove strong convergence theorems under shrinking projection methods for finding solutions of split common fixed point problems with zero points of maximal monotone operators in two Banach spaces. Using these results, we get new results which are connected with the split feasibility problem, the split common null point problem and the split common fixed point problem in Hilbert spaces and Banach spaces.

Author information

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

Wataru Takahashi

Research Center for Interneural Computing, China Medical University, Taichung, Taiwan
and: Keio Research and Education Center for Natural Sciences, Keio University, Yokohama, Japan
and: Dept. of Mathematical and Computing Sciences, Tokyo Inst. of Technology, Tokyo, Japan

wataru@is.titech.ac.jp

Jen-Chih Yao

Research Center for Interneural Computing, China Medical University, Taichung, Taiwan

yaojc@mail.cmu.edu.tw

Keywords

  • Split common fixed point problem
  • fixed point
  • metric projection
  • generalized projection
  • metric resolvent
  • generalized resolvent
  • shrinking projection method

Mathematics Subject Classification

47H05, 47H09

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Suggested citation

W. Takahashi, J.-C. Yao. “Strong Convergence Theorems under Shrinking Projection Methods for Split Common Fixed Point Problems in Two Banach Spaces.” Journal of Convex Analysis 28 (2021), No. 4, 1097–1118. https://doi.org/10.68381/jca28064

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