Infinite Product and Its Convergence in CAT(1) Spaces

Journal article

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Publication Details

Author list: Termkaew, Sakan; Chaipunya, Parin; Kohsaka, Fumiaki;

Publisher: MDPI

Publication year: 2023

Volume number: 11

Issue number: 8

ISSN: 22277390

eISSN: 2227-7390

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85153938359&doi=10.3390%2fmath11081807&partnerID=40&md5=620caf07419963e0b07b83ef1be8469b

Languages: English-Great Britain (EN-GB)

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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 (Formula presented.) -demiclosed mappings which covers finite products of strongly quasi-nonexpansive, (Formula presented.) -demiclosed mappings, and hence is applicable to the convergence of infinite products. © 2023 by the authors.

Keywords

CAT (1) space, strongly quasi-nonexpansive mapping