Open AccessThe periodic points of ε-contractive maps in fuzzy metric spaces
Author(s) -
Taixiang Sun,
Chunyan Han,
Guangwang Su,
Bin Qin,
Lue Li
Publication year - 2021
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2021.14449
Subject(s) - mathematics , metric space , metric (unit) , space (punctuation) , set (abstract data type) , point (geometry) , discrete mathematics , combinatorics , pure mathematics , geometry , linguistics , operations management , philosophy , economics , computer science , programming language
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.