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

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-10-01 DOI:10.4995/agt.2021.14449

T. Sun, Caihong Han, G. Su, Bin Qin, Lue Li

引用次数: 0

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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模糊度量空间中ε-压缩映射的周期点

本文引入模糊度量空间(X, M， *)上ε-压缩映射的概念，研究了ε-压缩映射的周期性。我们证明了如果(X, M，∗)是紧的，f: X−→X是ε-压缩的，则P(f) =∩∞n=1f n (X)，并且X的每个连通分量最多包含一个f的周期点，其中P(f)是f的周期点的集合。进一步，我们给出了两个例子来说明所得结果的适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.