Infinite Product and Its Convergence in CAT(1) Spaces
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/8/1807 |
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| author | Sakan Termkaew Parin Chaipunya Fumiaki Kohsaka |
| author_facet | Sakan Termkaew Parin Chaipunya Fumiaki Kohsaka |
| author_sort | Sakan Termkaew |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>-demiclosed mappings which covers finite products of strongly quasi-nonexpansive, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>-demiclosed mappings, and hence is applicable to the convergence of infinite products. |
| first_indexed | 2024-03-11T04:47:10Z |
| format | Article |
| id | doaj.art-ea180db7676e442f89b63bc00ae91f12 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:47:10Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ea180db7676e442f89b63bc00ae91f122023-11-17T20:16:45ZengMDPI AGMathematics2227-73902023-04-01118180710.3390/math11081807Infinite Product and Its Convergence in CAT(1) SpacesSakan Termkaew0Parin Chaipunya1Fumiaki Kohsaka2Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Mathematical Sciences, Faculty of Science, Tokai University, 4-1-1 Kitakaname, Hiratsuka 259-1292, JapanIn 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>-demiclosed mappings which covers finite products of strongly quasi-nonexpansive, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Δ</mo></semantics></math></inline-formula>-demiclosed mappings, and hence is applicable to the convergence of infinite products.https://www.mdpi.com/2227-7390/11/8/1807CAT (1) spaceconvex optimizationconvex feasibility problemstrongly quasi-nonexpansive mapping |
| spellingShingle | Sakan Termkaew Parin Chaipunya Fumiaki Kohsaka Infinite Product and Its Convergence in CAT(1) Spaces Mathematics CAT (1) space convex optimization convex feasibility problem strongly quasi-nonexpansive mapping |
| title | Infinite Product and Its Convergence in CAT(1) Spaces |
| title_full | Infinite Product and Its Convergence in CAT(1) Spaces |
| title_fullStr | Infinite Product and Its Convergence in CAT(1) Spaces |
| title_full_unstemmed | Infinite Product and Its Convergence in CAT(1) Spaces |
| title_short | Infinite Product and Its Convergence in CAT(1) Spaces |
| title_sort | infinite product and its convergence in cat 1 spaces |
| topic | CAT (1) space convex optimization convex feasibility problem strongly quasi-nonexpansive mapping |
| url | https://www.mdpi.com/2227-7390/11/8/1807 |
| work_keys_str_mv | AT sakantermkaew infiniteproductanditsconvergenceincat1spaces AT parinchaipunya infiniteproductanditsconvergenceincat1spaces AT fumiakikohsaka infiniteproductanditsconvergenceincat1spaces |