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Approximating Common Fixed Points of Nonexpansive Mappings on Hadamard Manifolds with Applications

Author

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  • Konrawut Khammahawong

    (Applied Mathematics for Science and Engineering Research Unit (AMSERU), Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand)

  • Parin Chaipunya

    (NCAO Research Center, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand)

  • Kamonrat Sombut

    (Applied Mathematics for Science and Engineering Research Unit (AMSERU), Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand)

Abstract

The point of this research is to present a new iterative procedure for approximating common fixed points of nonexpansive mappings in Hadamard manifolds. The convergence theorem of the proposed method is discussed under certain conditions. For the sake of clarity, we provide some numerical examples to support our results. Furthermore, we apply the suggested approach to solve inclusion problems and convex feasibility problems.

Suggested Citation

  • Konrawut Khammahawong & Parin Chaipunya & Kamonrat Sombut, 2022. "Approximating Common Fixed Points of Nonexpansive Mappings on Hadamard Manifolds with Applications," Mathematics, MDPI, vol. 10(21), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4080-:d:960907
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    References listed on IDEAS

    as
    1. Guo-ji Tang & Nan-jing Huang, 2012. "Korpelevich’s method for variational inequality problems on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 54(3), pages 493-509, November.
    2. Anantachai Padcharoen & Pakeeta Sukprasert, 2019. "Nonlinear Operators as Concerns Convex Programming and Applied to Signal Processing," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    3. O. Ferreira & L. Pérez & S. Németh, 2005. "Singularities of Monotone Vector Fields and an Extragradient-type Algorithm," Journal of Global Optimization, Springer, vol. 31(1), pages 133-151, January.
    4. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    5. Javid Ali & Faeem Ali & Puneet Kumar, 2019. "Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
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