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

Author

Listed:
  • Wachirapong Jirakitpuwapat

    (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
    These authors contributed equally to this work.)

  • Poom Kumam

    (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
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    These authors contributed equally to this work.)

  • Yeol Je Cho

    (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
    Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
    These authors contributed equally to this work.)

  • Kanokwan Sitthithakerngkiet

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

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).

Suggested Citation

  • Wachirapong Jirakitpuwapat & Poom Kumam & Yeol Je Cho & Kanokwan Sitthithakerngkiet, 2019. "A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:226-:d:209808
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    References listed on IDEAS

    as
    1. Boikanyo, Oganeditse A., 2015. "A strongly convergent algorithm for the split common fixed point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 844-853.
    2. NESTEROV, Yu., 2007. "Gradient methods for minimizing composite objective function," LIDAM Discussion Papers CORE 2007076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
    Full references (including those not matched with items on IDEAS)

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