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Open AccessArticle

Tseng Type Methods for Inclusion and Fixed Point Problems with Applications

by Raweerote Suparatulatorn 1,2,3,† and Anchalee Khemphet 1,2,3,*,†
1
Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2
Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand
3
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(12), 1175; https://doi.org/10.3390/math7121175
Received: 3 November 2019 / Revised: 21 November 2019 / Accepted: 26 November 2019 / Published: 3 December 2019
An algorithm is introduced to find an answer to both inclusion problems and fixed point problems. This algorithm is a modification of Tseng type methods inspired by Mann’s type iteration and viscosity approximation methods. On certain conditions, the iteration obtained from the algorithm converges strongly. Moreover, applications to the convex feasibility problem and the signal recovery in compressed sensing are considered. Especially, some numerical experiments of the algorithm are demonstrated. These results are compared to those of the previous algorithm. View Full-Text
Keywords: inclusion problem; fixed point problem; forward–backward splitting method; viscosity approximation method; Mann’s type iteration method inclusion problem; fixed point problem; forward–backward splitting method; viscosity approximation method; Mann’s type iteration method
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Suparatulatorn, R.; Khemphet, A. Tseng Type Methods for Inclusion and Fixed Point Problems with Applications. Mathematics 2019, 7, 1175.

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