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

Authors

  • Taixiang Sun Guangxi University of Finance and Economics
  • Lue Li Guangxi University of Finance and Economics
  • Guangwang Su Guangxi University of Finance and Economics
  • Caihong Han Guangxi University of Finance and Economics
  • Guoen Xia Guangxi University of Finance and Economics

DOI:

https://doi.org/10.4995/agt.2020.13126

Keywords:

fuzzy metric interval, attracting centre, depth

Abstract

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.

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Author Biographies

Taixiang Sun, Guangxi University of Finance and Economics

College of Information and Statistics

Lue Li, Guangxi University of Finance and Economics

College of Information and Statistics

Guangwang Su, Guangxi University of Finance and Economics

College of Information and Statistics

Caihong Han, Guangxi University of Finance and Economics

College of Information and Statistics

Guoen Xia, Guangxi University of Finance and Economics

College of of Business Administration

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Published

2020-10-01

How to Cite

[1]
T. Sun, L. Li, G. Su, C. Han, and G. Xia, “The depth and the attracting centre for a continuous map on a fuzzy metric interval”, Appl. Gen. Topol., vol. 21, no. 2, pp. 285–294, Oct. 2020.

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Articles