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Mathematics 2019, 7(3), 226; https://doi.org/10.3390/math7030226

A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing

1
KMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
2
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
5
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
6
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 24 December 2018 / Revised: 18 February 2019 / Accepted: 20 February 2019 / Published: 28 February 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
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Abstract

In 2014, Cui and Wang constructed an algorithm for demicontractive operators and proved some weak convergence theorems of their proposed algorithm to show the existence of solutions for the split common fixed point problem without using the operator norm. By Cui and Wang’s motivation, in 2015, Boikanyo constructed also a new algorithm for demicontractive operators and obtained some strong convergence theorems for this problem without using the operator norm. In this paper, we consider a viscosity iterative algorithm in Boikanyo’s algorithm to approximate to a solution of this problem and prove some strong convergence theorems of our proposed algorithm to a solution of this problem. Finally, we apply our main results to some applications, signal processing and others and compare our algorithm with five algorithms such as Cui and Wang’s algorithm, Boikanyo’s algorithm, forward-backward splitting algorithm and the fast iterative shrinkage-thresholding algorithm (FISTA). View Full-Text
Keywords: split common fixed point problem; demicontractive operator; Cui and Wang’s algorithm; Boikanyo’s algorithm; strong convergence split common fixed point problem; demicontractive operator; Cui and Wang’s algorithm; Boikanyo’s algorithm; strong convergence
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Jirakitpuwapat, W.; Kumam, P.; Cho, Y.J.; Sitthithakerngkiet, K. A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing. Mathematics 2019, 7, 226.

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