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

Authors

  • Taixiang Sun Guangxi University of Finance and Economics
  • Caihong Han Guangxi University of Finance and Economics
  • Guangwang Su Guangxi University of Finance and Economics
  • Bin Qin Guangxi (ASEAN)Research Center of Finance and Economics
  • Lue Li Guangxi University of Finance and Economics

DOI:

https://doi.org/10.4995/agt.2021.14449

Keywords:

fuzzy metric space, ε-contractive map, periodic point

Abstract

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.

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Author Biographies

Taixiang Sun, Guangxi University of Finance and Economics

College of Information and Statistics

Caihong Han, Guangxi University of Finance and Economics

College of Information and Statistics

Guangwang Su, Guangxi University of Finance and Economics

College of Information and Statistics

Lue Li, Guangxi University of Finance and Economics

College of Information and Statistics

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Published

2021-10-01

How to Cite

[1]
T. Sun, C. Han, G. Su, B. Qin, and L. Li, “The periodic points of ε-contractive maps in fuzzy metric spaces”, Appl. Gen. Topol., vol. 22, no. 2, pp. 311–319, Oct. 2021.

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Section

Regular Articles