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
• DOI: 10.4995/agt.2021.14449
• Enlaces
  • Texto completo
• 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.

• Referencias bibliográficas
  • M. Abbas, M. Imdad and D. Gopal, ψ-weak contractions in fuzzy metric spaces, Iranian J. Fuzzy Syst. 8 (2011), 141-148.
  • I. Beg, C. Vetro, D, Gopal and M. Imdad, (Φ, ψ)-weak contractions in intuitionistic fuzzy metric spaces, J. Intel. Fuzzy Syst. 26 (2014),...
  • A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  • M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1989), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
  • V. Gregori and J. J. Miñana, Some remarks on fuzzy contractive mappings, Fuzzy Sets Syst. 251 (2014), 101-103. https://doi.org/10.1016/j.fss.2014.01.002
  • V. Gregori and J. J. Miñana, On fuzzy $Psi$-contractive sequences and fixed point theorems, Fuzzy Sets Syst. 300 (2016), 93-101. https://doi.org/10.1016/j.fss.2015.12.010
  • V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets Syst. 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9
  • J. Harjani, B. López and K. Sadarangani, Fixed point theorems for cyclic weak contractions in compact metric spaces, J. Nonl. Sci. Appl. 6...
  • X. Hu, Z. Mo and Y. Zhen, On compactnesses of fuzzy metric spaces (Chinese), J. Sichuan Norm. Univer. (Natur. Sei.) 32 (2009), 184-187.
  • I. Kramosil and J. Michàlek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), 336-344.
  • D. Mihet, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets Sys. 159 (2008), 739-744. https://doi.org/10.1016/j.fss.2007.07.006
  • D. Mihet, A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets Syst. 251 (2014), 83-91. https://doi.org/10.1016/j.fss.2014.04.010
  • B. Schweizer and A. Sklar, Statistical metrics paces, Pacif. J. Math. 10 (1960), 385-389. https://doi.org/10.2140/pjm.1960.10.313
  • Y. Shen, D. Qiu and W. Chen, Fixed point theorems in fuzzy metric spaces, Appl. Math. Letters 25 (2012), 138-141. https://doi.org/10.1016/j.aml.2011.08.002
  • S. Shukla, D. Gopal and A. F. Roldán-López-de-Hierro, Some fixed point theorems in 1-M-complete fuzzy metric-like spaces, Inter. J. General...
  • S. Shukla, D. Gopal and W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets Syst. 359 (2018),...
  • D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222 (2013), 108-114. https://doi.org/10.1016/j.fss.2013.01.012
  • D. Zheng and P. Wang, On probabilistic Ψ-contractions in Menger probabilistic metric spaces, Fuzzy Sets Syst. 350 (2018), 107-110. https://doi.org/10.1016/j.fss.2018.02.011
  • D. Zheng and P. Wang, Meir-Keeler theorems in fuzzy metric spaces, Fuzzy Sets Syst. 370 (2019), 120-128. https://doi.org/10.1016/j.fss.2018.08.014