Infinite Product and Its Convergence in CAT(1) Spaces

Sakan Termkaew, Parin Chaipunya () and Fumiaki Kohsaka
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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
Fumiaki Kohsaka: Department of Mathematical Sciences, Faculty of Science, Tokai University, 4-1-1 Kitakaname, Hiratsuka 259-1292, Japan

Mathematics, 2023, vol. 11, issue 8, 1-17

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.

Keywords: CAT (1) space; convex optimization; convex feasibility problem; strongly quasi-nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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