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Two Projection Algorithms for Solving the Split Common Fixed Point Problem

Author

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  • Simeon Reich

    (The Technion – Israel Institute of Technology)

  • Truong Minh Tuyen

    (Thai Nguyen University of Science)

Abstract

We study the split common fixed point problem for Bregman relatively nonexpansive operators in real reflexive Banach spaces. Using Bregman distances, we propose two new projection algorithms for solving this problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01702-0
    DOI: 10.1007/s10957-020-01702-0
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    References listed on IDEAS

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    1. Mohammed Ali Alghamdi & Naseer Shahzad & Habtu Zegeye, 2014. "Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, July.
    2. H. Zegeye & N. Shahzad, 2014. "Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, May.
    3. 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.
    4. 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.
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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.

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