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

• Sun, Taixiang ^[1] ; Han, Caihong ^[1] ; Su, Guangwang ^[1] ; Qin, Bin ^[2] ; Li, Lue ^[1]
  1. [1] Guangxi University of Finance and Economics

     Guangxi University of Finance and Economics

     China

     
  2. [2] Guangxi (ASEAN）Research Center of Finance and Economics
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 2, 2021, págs. 311-319
• Idioma: inglés
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• Resumen

  • 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.