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Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems

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  • Nattakarn Kaewyong

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand)

  • Kanokwan Sitthithakerngkiet

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand)

Abstract

In this paper, we study a monotone inclusion problem in the framework of Hilbert spaces. (1) We introduce a new modified Tseng’s method that combines inertial and viscosity techniques. Our aim is to obtain an algorithm with better performance that can be applied to a broader class of mappings. (2) We prove a strong convergence theorem to approximate a solution to the monotone inclusion problem under some mild conditions. (3) We present a modified version of the proposed iterative scheme for solving convex minimization problems. (4) We present numerical examples that satisfy the image restoration problem and illustrate our proposed algorithm’s computational performance.

Suggested Citation

  • Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2021. "Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1104-:d:553912
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    References listed on IDEAS

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    1. Prasit Cholamjiak & Suthep Suantai, 2012. "Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions," Journal of Global Optimization, Springer, vol. 54(1), pages 185-197, September.
    2. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
    3. Mujahid Abbas & Yusuf Ibrahim & Abdul Rahim Khan & Manuel De la Sen, 2019. "Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT (0) Spaces," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
    4. Chanjuan Pan & Yuanheng Wang, 2019. "Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces," Mathematics, MDPI, vol. 7(5), pages 1-13, April.
    5. Sitthithakerngkiet, Kanokwan & Deepho, Jitsupa & Kumam, Poom, 2015. "A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 986-1001.
    6. Adisak Hanjing & Suthep Suantai, 2020. "A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
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