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Common Attractive Point Results for Two Generalized Nonexpansive Mappings in Uniformly Convex Banach Spaces

Author

Listed:
  • Chadarat Thongphaen

    (Master’s Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Warunun Inthakon

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Suthep Suantai

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Narawadee Phudolsitthiphat

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

In this work, we study some basic properties of the set of common attractive points and prove strong convergence results for common attractive points of two generalized nonexpansive mappings in a uniformly convex Banach space. As a consequence, we obtain a common fixed point result of such mappings and apply it to solving the convex minimization problem. Finally, numerical experiments are given to support our results.

Suggested Citation

  • Chadarat Thongphaen & Warunun Inthakon & Suthep Suantai & Narawadee Phudolsitthiphat, 2022. "Common Attractive Point Results for Two Generalized Nonexpansive Mappings in Uniformly Convex Banach Spaces," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1275-:d:792063
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    References listed on IDEAS

    as
    1. Dawan Chumpungam & Panitarn Sarnmeta & Suthep Suantai, 2021. "A New Forward–Backward Algorithm with Line Searchand Inertial Techniques for Convex Minimization Problems with Applications," Mathematics, MDPI, vol. 9(13), pages 1-20, July.
    2. Panadda Thongpaen & Attapol Kaewkhao & Narawadee Phudolsitthiphat & Suthep Suantai & Warunun Inthakon, 2021. "Weak and Strong Convergence Theorems for Common Attractive Points of Widely More Generalized Hybrid Mappings in Hilbert Spaces," Mathematics, MDPI, vol. 9(19), pages 1-12, October.
    3. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    4. Entisarat El-Shobaky & Sahar Mohammed Ali & Wataru Takahashi, 2001. "On projection constant problems and the existence of metric projections in normed spaces," Abstract and Applied Analysis, Hindawi, vol. 6, pages 1-11, January.
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