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Approximating Fixed Points of Bregman Generalized α -Nonexpansive Mappings

Author

Listed:
  • Kanikar Muangchoo

    (KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand)

  • Poom Kumam

    (KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Yeol Je Cho

    (Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Sompong Dhompongsa

    (KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Sakulbuth Ekvittayaniphon

    (Rajamangala University of Technology Phra Nakhon, 399 Samsen Rd., Vachira Phayaban, Dusit, Bangkok 10300, Thailand)

Abstract

In this paper, we introduce a new class of Bregman generalized α -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized α -nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results of fixed point approximation using Halpern’s algorithm.

Suggested Citation

  • Kanikar Muangchoo & Poom Kumam & Yeol Je Cho & Sompong Dhompongsa & Sakulbuth Ekvittayaniphon, 2019. "Approximating Fixed Points of Bregman Generalized α -Nonexpansive Mappings," Mathematics, MDPI, vol. 7(8), pages 1-28, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:709-:d:255279
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    References listed on IDEAS

    as
    1. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    2. Dan Butnariu & Elena Resmerita, 2006. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-39, February.
    3. Chin-Tzong Pang & Eskandar Naraghirad & Ching-Feng Wen, 2014. "Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, May.
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