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Infinite Product and Its Convergence in CAT(1) Spaces

Author

Listed:
  • Sakan Termkaew

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand)

  • Parin Chaipunya

    (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), King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand)

  • Fumiaki Kohsaka

    (Department of Mathematical Sciences, Faculty of Science, Tokai University, 4-1-1 Kitakaname, Hiratsuka 259-1292, Japan)

Abstract

In this paper, we study the convergence of infinite product of strongly quasi-nonexpansive mappings on geodesic spaces with curvature bounded above by one. Our main applications behind this study are to solve convex feasibility by alternating projections, and to solve minimizers of convex functions and common minimizers of several objective functions. To prove our main results, we introduce a new concept of orbital Δ -demiclosed mappings which covers finite products of strongly quasi-nonexpansive, Δ -demiclosed mappings, and hence is applicable to the convergence of infinite products.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1807-:d:1120505
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    References listed on IDEAS

    as
    1. 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.
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