Iterative Methods for Finding Solutions of a Class of Split Feasibility Problems over Fixed Point Sets in Hilbert Spaces

Suthep Suantai, Narin Petrot and Montira Suwannaprapa
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Suthep Suantai: Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Narin Petrot: Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Montira Suwannaprapa: Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna, Chiang Rai 57120, Thailand

Mathematics, 2019, vol. 7, issue 11, 1-21

Abstract: We consider the split feasibility problem in Hilbert spaces when the hard constraint is common solutions of zeros of the sum of monotone operators and fixed point sets of a finite family of nonexpansive mappings, while the soft constraint is the inverse image of a fixed point set of a nonexpansive mapping. We introduce iterative algorithms for the weak and strong convergence theorems of the constructed sequences. Some numerical experiments of the introduced algorithm are also discussed.

Keywords: split feasibility problem; fixed point problem; inverse strongly monotone operator; maximal monotone operator; iterative methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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