Journal of Convex Analysis 28 (2021), No. 4, 1097--1118
Copyright Heldermann Verlag 2021
Strong Convergence Theorems under Shrinking Projection Methods for Split Common Fixed Point Problems in Two Banach Spaces
Wataru Takahashi
Research Center for Interneural Computing, China Medical University, Taichung, Taiwan
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
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.
Keywords: Split common fixed point problem, fixed point, metric projection, generalized projection, metric resolvent, generalized resolvent, shrinking projection method.
MSC: 47H05, 47H09.
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