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A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing

Author

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  • Yinglin Luo

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Meijuan Shang

    (College of Science, Shijiazhuang University, Shijiazhuang 050035, China)

  • Bing Tan

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.

Suggested Citation

  • Yinglin Luo & Meijuan Shang & Bing Tan, 2020. "A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing," Mathematics, MDPI, vol. 8(2), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:288-:d:322947
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    References listed on IDEAS

    as
    1. Yu. Malitsky & V. Semenov, 2015. "A hybrid method without extrapolation step for solving variational inequality problems," Journal of Global Optimization, Springer, vol. 61(1), pages 193-202, January.
    2. Xiaolong Qin & Nguyen Thai An, 2019. "Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets," Computational Optimization and Applications, Springer, vol. 74(3), pages 821-850, December.
    3. Nguyen Thai An & Nguyen Mau Nam & Xiaolong Qin, 2020. "Solving k-center problems involving sets based on optimization techniques," Journal of Global Optimization, Springer, vol. 76(1), pages 189-209, January.
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    Cited by:

    1. Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "Strong Convergent Theorems Governed by Pseudo-Monotone Mappings," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    2. Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "A Hybrid Forward–Backward Algorithm and Its Optimization Application," Mathematics, MDPI, vol. 8(3), pages 1-16, March.

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