The periodic points of ε-contractive maps in fuzzy metric spaces

The periodic points of ε-contractive maps in fuzzy metric spaces

In this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one perio...

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Main Authors: Taixiang Sun, Caihong Han, Guangwang Su, Bin Qin, Lue Li
Format: Article
Language:English
Published: Universitat Politècnica de València 2021-10-01
Series:Applied General Topology
Subjects:
fuzzy metric space
ε-contractive map
periodic point
Online Access:https://polipapers.upv.es/index.php/AGT/article/view/14449
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spelling doaj-7952308e845c442f9df5017bb84e67422021-10-04T11:53:16ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472021-10-0122231131910.4995/agt.2021.144499030The periodic points of ε-contractive maps in fuzzy metric spacesTaixiang Sun0Caihong Han1Guangwang Su2Bin Qin3Lue Li4Guangxi University of Finance and EconomicsGuangxi University of Finance and EconomicsGuangxi University of Finance and EconomicsGuangxi (ASEAN）Research Center of Finance and EconomicsGuangxi University of Finance and EconomicsIn this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points of f. Furthermore, we present two examples to illustrate the applicability of the obtained results.https://polipapers.upv.es/index.php/AGT/article/view/14449fuzzy metric spaceε-contractive mapperiodic point
collection DOAJ
language English
format Article
sources DOAJ
author Taixiang Sun
Caihong Han
Guangwang Su
Bin Qin
Lue Li
spellingShingle Taixiang Sun
Caihong Han
Guangwang Su
Bin Qin
Lue Li
The periodic points of ε-contractive maps in fuzzy metric spaces
Applied General Topology
fuzzy metric space
ε-contractive map
periodic point
author_facet Taixiang Sun
Caihong Han
Guangwang Su
Bin Qin
Lue Li
author_sort Taixiang Sun
title The periodic points of ε-contractive maps in fuzzy metric spaces
title_short The periodic points of ε-contractive maps in fuzzy metric spaces
title_full The periodic points of ε-contractive maps in fuzzy metric spaces
title_fullStr The periodic points of ε-contractive maps in fuzzy metric spaces
title_full_unstemmed The periodic points of ε-contractive maps in fuzzy metric spaces
title_sort periodic points of ε-contractive maps in fuzzy metric spaces
publisher Universitat Politècnica de València
series Applied General Topology
issn 1576-9402
1989-4147
publishDate 2021-10-01
description In this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points of f. Furthermore, we present two examples to illustrate the applicability of the obtained results.
topic fuzzy metric space
ε-contractive map
periodic point
url https://polipapers.upv.es/index.php/AGT/article/view/14449
work_keys_str_mv AT taixiangsun theperiodicpointsofecontractivemapsinfuzzymetricspaces
AT caihonghan theperiodicpointsofecontractivemapsinfuzzymetricspaces
AT guangwangsu theperiodicpointsofecontractivemapsinfuzzymetricspaces
AT binqin theperiodicpointsofecontractivemapsinfuzzymetricspaces
AT lueli theperiodicpointsofecontractivemapsinfuzzymetricspaces
AT taixiangsun periodicpointsofecontractivemapsinfuzzymetricspaces
AT caihonghan periodicpointsofecontractivemapsinfuzzymetricspaces
AT guangwangsu periodicpointsofecontractivemapsinfuzzymetricspaces
AT binqin periodicpointsofecontractivemapsinfuzzymetricspaces
AT lueli periodicpointsofecontractivemapsinfuzzymetricspaces
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