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

Taixiang Sun

China

Guangxi University of Finance and Economics

College of Information and Statistics

Lue Li

China

Guangxi University of Finance and Economics

College of Information and Statistics

Guangwang Su

China

Guangxi University of Finance and Economics

College of Information and Statistics

Caihong Han

China

Guangxi University of Finance and Economics

College of Information and Statistics

Guoen Xia

China

Guangxi University of Finance and Economics

College of of Business Administration
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Accepted: 2020-05-11

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Published: 2020-10-01

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

fuzzy metric interval, attracting centre, depth

Supporting agencies:

NNSF of China (11761011

71862003)

NSF of Guangxi (2018GXNSFAA294010)

SF of Guangxi University of Finance and Economics (2019QNB10)

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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