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

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Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
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Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
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Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
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Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna, Chiang Rai 57120, Thailand
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1012; https://doi.org/10.3390/math7111012
Received: 9 September 2019 / Revised: 16 October 2019 / Accepted: 22 October 2019 / Published: 24 October 2019
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. View Full-Text
Keywords: split feasibility problem; fixed point problem; inverse strongly monotone operator; maximal monotone operator; iterative methods split feasibility problem; fixed point problem; inverse strongly monotone operator; maximal monotone operator; iterative methods
MDPI and ACS Style

Suantai, S.; Petrot, N.; Suwannaprapa, M. Iterative Methods for Finding Solutions of a Class of Split Feasibility Problems over Fixed Point Sets in Hilbert Spaces. Mathematics 2019, 7, 1012.

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