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Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces

In: Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author

Listed:
  • Simeon Reich

    (The Technion – Israel Institute of Technology)

  • Shoham Sabach

Abstract

We study the existence and approximation of fixed points of Bregman firmly nonexpansive mappings in reflexive Banach spaces.

Suggested Citation

  • Simeon Reich & Shoham Sabach, 2011. "Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces," 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 301-316, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-9569-8_15
    DOI: 10.1007/978-1-4419-9569-8_15
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    Citations

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    Cited by:

    1. Simeon Reich & Truong Minh Tuyen, 2021. "Projection Algorithms for Solving the Split Feasibility Problem with Multiple Output Sets," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 861-878, September.
    2. Jiawei Chen & Zhongping Wan & Liuyang Yuan & Yue Zheng, 2011. "Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-23, July.
    3. Simeon Reich & Truong Minh Tuyen, 2020. "Two Projection Algorithms for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 148-168, July.
    4. Vahid Darvish, 2016. "Strong convergence theorem for a system of generalized mixed equilibrium problems and finite family of Bregman nonexpansive mappings in Banach spaces," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 584-603, September.
    5. Kumar, Ajay & Thakur, Balwant Singh & Postolache, Mihai, 2024. "Dynamic stepsize iteration process for solving split common fixed point problems with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 498-511.

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