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The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings

Author

Listed:
  • David Ariza-Ruiz

    (Universidad de Sevilla)

  • Genaro López-Acedo

    (Universidad de Sevilla)

  • Adriana Nicolae

    (Babeş-Bolyai University
    Simion Stoilow Institute of Mathematics of the Romanian Academy, Research group of the project PD-3-0152)

Abstract

In this paper, we provide, in the setting of geodesic spaces, a unified treatment of some convex minimization problems, which allows for a better understanding and, in some cases, improvement of results proved recently in this direction. For this purpose, we analyze the asymptotic behavior of compositions of finitely many firmly nonexpansive mappings focusing on asymptotic regularity and convergence results.

Suggested Citation

  • David Ariza-Ruiz & Genaro López-Acedo & Adriana Nicolae, 2015. "The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 409-429, November.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-015-0710-3
    DOI: 10.1007/s10957-015-0710-3
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    Citations

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    Cited by:

    1. Laurenţiu Leuştean & Adriana Nicolae & Andrei Sipoş, 2018. "An abstract proximal point algorithm," Journal of Global Optimization, Springer, vol. 72(3), pages 553-577, November.
    2. Andrei Sipoş, 2022. "Abstract strongly convergent variants of the proximal point algorithm," Computational Optimization and Applications, Springer, vol. 83(1), pages 349-380, September.
    3. Ítalo Dowell Lira Melo & João Xavier Cruz Neto & José Márcio Machado Brito, 2022. "Strong Convergence of Alternating Projections," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 306-324, July.
    4. Byoung Jin Choi, 2020. "Δ-Convergence of Products of Operators in p -Uniformly Convex Metric Spaces," Mathematics, MDPI, vol. 8(5), pages 1-8, May.
    5. Sakan Termkaew & Parin Chaipunya & Fumiaki Kohsaka, 2023. "Infinite Product and Its Convergence in CAT(1) Spaces," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
    6. José Márcio Machado Brito & João Xavier Cruz Neto & Ítalo Dowell Lira Melo, 2024. "Strong convergence of the composition of firmly nonexpansive mappings," Journal of Global Optimization, Springer, vol. 90(4), pages 891-907, December.
    7. Alexander Lytchak & Anton Petrunin, 2022. "Cyclic Projections in Hadamard Spaces," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 636-642, August.

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