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Inertial viscosity-type iterative method for solving inclusion problems with applications

Author

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  • Adamu, A.
  • Kitkuan, D.
  • Padcharoen, A.
  • Chidume, C.E.
  • Kumam, P.

Abstract

An inertial viscosity-type iterative method that approximates a solution of an inclusion problem and a fixed point problem is introduced and studied. Strong convergence theorem is proved in some Banach spaces. The theorem proved is applied to image restoration, convex minimization and signal processing problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

Suggested Citation

  • Adamu, A. & Kitkuan, D. & Padcharoen, A. & Chidume, C.E. & Kumam, P., 2022. "Inertial viscosity-type iterative method for solving inclusion problems with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 445-459.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:445-459
    DOI: 10.1016/j.matcom.2021.12.007
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    References listed on IDEAS

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    1. 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.
    2. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    3. S. Takahashi & W. Takahashi & M. Toyoda, 2010. "Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 27-41, October.
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    Cited by:

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    2. Zhaoteng Chu & Chenliang Li, 2023. "Overlapping Domain Decomposition Method with Cascadic Multigrid for Image Restoration," Mathematics, MDPI, vol. 11(10), pages 1-14, May.

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