The depth and the attracting centre for a continuous map on a fuzzy metric interval

[EN] Let I be a fuzzy metric interval and f be a continuous map from I to I. Denote by R(f), Ω(f) and ω(x, f) the set of recurrent points of f, the set of non-wandering points of f and the set of ω- limit points of x under f, respectively. Write ω(f) = ∪x∈Iω(x, f), ωn+1(f) = ∪x∈ωn(f)ω(x, f) and Ωn+1...

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Detalles Bibliográficos
Autores: Sun, Taixiang, Li, Lue, Su, Guangwang, Han, Caihong, Xia, Guoen
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/151365
Acceso en línea:https://riunet.upv.es/handle/10251/151365
Access Level:acceso abierto
Palabra clave:Fuzzy metric interval
Attracting centre
Depth
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spelling The depth and the attracting centre for a continuous map on a fuzzy metric intervalSun, TaixiangLi, LueSu, GuangwangHan, CaihongXia, GuoenFuzzy metric intervalAttracting centreDepth[EN] Let I be a fuzzy metric interval and f be a continuous map from I to I. Denote by R(f), Ω(f) and ω(x, f) the set of recurrent points of f, the set of non-wandering points of f and the set of ω- limit points of x under f, respectively. Write ω(f) = ∪x∈Iω(x, f), ωn+1(f) = ∪x∈ωn(f)ω(x, f) and Ωn+1(f) = Ω(f|Ωn(f)) for any positive integer n. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2, and ω3(f) = ω2(f) and the depth of the attracting centre of f is at most 2.Project supported by NNSF of China (11761011, 71862003) and NSF of Guangxi (2018GXNSFAA294010) and SF of Guangxi University of Finance and Economics (2019QNB10).Universitat Politècnica de ValènciaNational Natural Science Foundation of ChinaNational Science Foundation, ChinaCentral University of Finance and Economics, ChinaRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/151365reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengNational Natural Science Foundation of China https://doi.org/10.13039/501100001809 71862003National Natural Science Foundation of China https://doi.org/10.13039/501100001809 11761011National Natural Science Foundation of China https://doi.org/10.13039/501100001809 2018GXNSFAA294010Central University of Finance and Economics, China https://doi.org/10.13039/501100002942 2019QNB10open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1513652026-06-13T07:49:27Z
dc.title.none.fl_str_mv The depth and the attracting centre for a continuous map on a fuzzy metric interval
title The depth and the attracting centre for a continuous map on a fuzzy metric interval
spellingShingle The depth and the attracting centre for a continuous map on a fuzzy metric interval
Sun, Taixiang
Fuzzy metric interval
Attracting centre
Depth
title_short The depth and the attracting centre for a continuous map on a fuzzy metric interval
title_full The depth and the attracting centre for a continuous map on a fuzzy metric interval
title_fullStr The depth and the attracting centre for a continuous map on a fuzzy metric interval
title_full_unstemmed The depth and the attracting centre for a continuous map on a fuzzy metric interval
title_sort The depth and the attracting centre for a continuous map on a fuzzy metric interval
dc.creator.none.fl_str_mv Sun, Taixiang
Li, Lue
Su, Guangwang
Han, Caihong
Xia, Guoen
author Sun, Taixiang
author_facet Sun, Taixiang
Li, Lue
Su, Guangwang
Han, Caihong
Xia, Guoen
author_role author
author2 Li, Lue
Su, Guangwang
Han, Caihong
Xia, Guoen
author2_role author
author
author
author
dc.contributor.none.fl_str_mv National Natural Science Foundation of China
National Science Foundation, China
Central University of Finance and Economics, China
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Fuzzy metric interval
Attracting centre
Depth
topic Fuzzy metric interval
Attracting centre
Depth
description [EN] Let I be a fuzzy metric interval and f be a continuous map from I to I. Denote by R(f), Ω(f) and ω(x, f) the set of recurrent points of f, the set of non-wandering points of f and the set of ω- limit points of x under f, respectively. Write ω(f) = ∪x∈Iω(x, f), ωn+1(f) = ∪x∈ωn(f)ω(x, f) and Ωn+1(f) = Ω(f|Ωn(f)) for any positive integer n. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2, and ω3(f) = ω2(f) and the depth of the attracting centre of f is at most 2.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/151365
url https://riunet.upv.es/handle/10251/151365
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv National Natural Science Foundation of China https://doi.org/10.13039/501100001809 71862003
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 11761011
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 2018GXNSFAA294010
Central University of Finance and Economics, China https://doi.org/10.13039/501100002942 2019QNB10
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de València
publisher.none.fl_str_mv Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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