Abstract

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.

Author information

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

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

wataru@is.titech.ac.jp

Keywords

  • Split common fixed point problem
  • fixed point
  • metric projection
  • metric resolvent
  • shrinking projection method
  • duality mapping

Mathematics Subject Classification

47H05, 47H09

Suggested citation

W. Takahashi. “The Split Common Fixed Point Problem and the Shrinking Projection Method in Banach Spaces.” Journal of Convex Analysis 24 (2017), No. 3, 1015–1028.

Copyright Banach Press 2017