Infinite Product and Its Convergence in CAT(1) Spaces-Reference-Cited by-同舟云学术

Infinite Product and Its Convergence in CAT(1) Spaces

Published:2023-04-11 Issue:8 Volume:11 Page:1807
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Termkaew Sakan¹,Chaipunya Parin¹²,Kohsaka Fumiaki³

Affiliation:

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

2. 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

3. 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.

Funder

King Mongkut’s University of Technology Thonburi

Thailand Science Research and Innovation (TSRI) Basic Research Fund

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/8/1807/pdf

Reference27 articles.

1. Nonexpansive projections and resolvents of accretive operators in Banach spaces;Bruck;Houston J. Math.,1977

2. Random products of contractions in metric and Banach spaces;Bruck;J. Math. Anal. Appl.,1982

3. Firmly nonexpansive mappings in classes of geodesic spaces;Trans. Amer. Math. Soc.,2014

4. Halpern iteration for strongly quasinonexpansive mappings on a geodesic space with curvature bounded above by one;Kimura;Fixed Point Theory Appl.,2013

5. Alternating projections in CAT(0) spaces;Searston;J. Math. Anal. Appl.,2012