The depth and the attracting centre for a continuous map on a fuzzy metric interval
Submitted: 2020-02-13
|Accepted: 2020-05-11
|Published: 2020-10-01
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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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