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

Taixiang Sun; Lue Li; Guangwang Su; Caihong Han; Guoen Xia

doi:10.4995/agt.2020.13126

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) = âˆªxâˆˆIω(x, f), ωn+1(f) = âˆªxâˆˆωn(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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