Polynomial-like iterative equation on Riesz spaces
In this paper we investigate the polynomial-like iterative equation on Riesz spaces. Since a Riesz space does not need to have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point theorem is available. Using the Knaster–Tarski fixed point theorem, we first ob...
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| Veröffentlicht in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis 2024-09, Vol.28 (4), p.55, Article 55 |
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| container_title | Positivity : an international journal devoted to the theory and applications of positivity in analysis |
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| creator | Gopalakrishna, Chaitanya Zhang, Weinian |
| description | In this paper we investigate the polynomial-like iterative equation on Riesz spaces. Since a Riesz space does not need to have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point theorem is available. Using the Knaster–Tarski fixed point theorem, we first obtain the existence and uniqueness of order-preserving solutions on convex complete sublattices of Riesz spaces. Then, restricting to
R
and
R
n
, special cases of Riesz space, we obtain semi-continuous solutions and integrable solutions, respectively. Finally, we present more special cases of Riesz space in which solutions to the iterative equation can be discussed. |
| doi_str_mv | 10.1007/s11117-024-01072-1 |
| format | Article |
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R
and
R
n
, special cases of Riesz space, we obtain semi-continuous solutions and integrable solutions, respectively. Finally, we present more special cases of Riesz space in which solutions to the iterative equation can be discussed.</description><identifier>ISSN: 1385-1292</identifier><identifier>EISSN: 1572-9281</identifier><identifier>DOI: 10.1007/s11117-024-01072-1</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Calculus of Variations and Optimal Control; Optimization ; Econometrics ; Euclidean space ; Fixed points (mathematics) ; Fourier Analysis ; Mathematical functions ; Mathematics ; Mathematics and Statistics ; Metric space ; Operator Theory ; Polynomials ; Potential Theory ; Schauder fixpoint theorem ; Uniqueness theorems</subject><ispartof>Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2024-09, Vol.28 (4), p.55, Article 55</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-94c71f4bc66d9223eb58e4192c02f7752ab3242cf75231723fa76474746c0d963</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11117-024-01072-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11117-024-01072-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Gopalakrishna, Chaitanya</creatorcontrib><creatorcontrib>Zhang, Weinian</creatorcontrib><title>Polynomial-like iterative equation on Riesz spaces</title><title>Positivity : an international journal devoted to the theory and applications of positivity in analysis</title><addtitle>Positivity</addtitle><description>In this paper we investigate the polynomial-like iterative equation on Riesz spaces. Since a Riesz space does not need to have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point theorem is available. Using the Knaster–Tarski fixed point theorem, we first obtain the existence and uniqueness of order-preserving solutions on convex complete sublattices of Riesz spaces. Then, restricting to
R
and
R
n
, special cases of Riesz space, we obtain semi-continuous solutions and integrable solutions, respectively. Finally, we present more special cases of Riesz space in which solutions to the iterative equation can be discussed.</description><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Econometrics</subject><subject>Euclidean space</subject><subject>Fixed points (mathematics)</subject><subject>Fourier Analysis</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Metric space</subject><subject>Operator Theory</subject><subject>Polynomials</subject><subject>Potential Theory</subject><subject>Schauder fixpoint theorem</subject><subject>Uniqueness theorems</subject><issn>1385-1292</issn><issn>1572-9281</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LxDAQDaLguvoHPBU8RyeTtGmOsvgFC4roOaTZVLp2292kFdZf72gFb84H8w7vvYHH2LmASwGgr5Kg0hxQcRCgkYsDNhM5AYOlOCQsy5wLNHjMTlJaA7FAwYzhU9_uu37TuJa3zXvImiFENzQfIQu7kUDfZTTPTUifWdo6H9IpO6pdm8LZ752z19ubl8U9Xz7ePSyul9wjwMCN8lrUqvJFsTKIMlR5GZQw6AFrrXN0lUSFviYohUZZO10oTV14WJlCztnF5LuN_W4MabDrfowdvbQSSinB0BILJ5aPfUox1HYbm42LeyvAfmdjp2wsZWN_srGCRHISJSJ3byH-Wf-j-gJDQWSa</recordid><startdate>20240901</startdate><enddate>20240901</enddate><creator>Gopalakrishna, Chaitanya</creator><creator>Zhang, Weinian</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20240901</creationdate><title>Polynomial-like iterative equation on Riesz spaces</title><author>Gopalakrishna, Chaitanya ; Zhang, Weinian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-94c71f4bc66d9223eb58e4192c02f7752ab3242cf75231723fa76474746c0d963</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Econometrics</topic><topic>Euclidean space</topic><topic>Fixed points (mathematics)</topic><topic>Fourier Analysis</topic><topic>Mathematical functions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Metric space</topic><topic>Operator Theory</topic><topic>Polynomials</topic><topic>Potential Theory</topic><topic>Schauder fixpoint theorem</topic><topic>Uniqueness theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gopalakrishna, Chaitanya</creatorcontrib><creatorcontrib>Zhang, Weinian</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Positivity : an international journal devoted to the theory and applications of positivity in analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gopalakrishna, Chaitanya</au><au>Zhang, Weinian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Polynomial-like iterative equation on Riesz spaces</atitle><jtitle>Positivity : an international journal devoted to the theory and applications of positivity in analysis</jtitle><stitle>Positivity</stitle><date>2024-09-01</date><risdate>2024</risdate><volume>28</volume><issue>4</issue><spage>55</spage><pages>55-</pages><artnum>55</artnum><issn>1385-1292</issn><eissn>1572-9281</eissn><abstract>In this paper we investigate the polynomial-like iterative equation on Riesz spaces. Since a Riesz space does not need to have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point theorem is available. Using the Knaster–Tarski fixed point theorem, we first obtain the existence and uniqueness of order-preserving solutions on convex complete sublattices of Riesz spaces. Then, restricting to
R
and
R
n
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| ispartof | Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2024-09, Vol.28 (4), p.55, Article 55 |
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| subjects | Calculus of Variations and Optimal Control Optimization Econometrics Euclidean space Fixed points (mathematics) Fourier Analysis Mathematical functions Mathematics Mathematics and Statistics Metric space Operator Theory Polynomials Potential Theory Schauder fixpoint theorem Uniqueness theorems |
| title | Polynomial-like iterative equation on Riesz spaces |
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