Fixed points which belong to the set of unit values of a suitable function on fuzzy metric spaces

• Saleh, Hayel N. ^[1] ; Imdad, Mohammad ^[1] ; Sintunavarat, Wutiphol ^[2]
  1. [1] Aligarh Muslim University

     Aligarh Muslim University

     India

     
  2. [2] Thammasat University

     Thammasat University

     Tailandia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 1, 2023, págs. 9-24
• Idioma: inglés
• DOI: 10.4995/agt.2023.16924
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we introduce the notion of fuzzy (F, φ,β-ψ)-contractive mappings in fuzzy metric spaces and utilize the same to prove some existence and uniqueness fuzzy φ-fixed point results in both M-complete and G-complete fuzzy metric spaces. The obtained results extend, generalize and improve some relevant results of the existing literature. An illustrative example is utilized to demonstrate the usefulness and effectiveness of our results.

• Referencias bibliográficas
  • M. Abbas, M. Imdad and D. Gopal, ψ-weak contractions in fuzzy metric spaces, Iranian Journal of Fuzzy Systems 8 (2011), 141-148.
  • G. Babu, K. Sarma and Y. G. Aemro, Generalization of fixed point results for (α,η,β)-contractive mappings in fuzzy metric spaces, Bangmod...
  • Z. Deng, Fuzzy pseudo-metric spaces, Journal of Mathematical Analysis and Applications 86 (1982), 74-95. https://doi.org/10.1016/0022-247X(82)90255-4
  • M. A. Erceg, Metric spaces in fuzzy set theory, Journal of Mathematical Analysis and Applications 69 (1979), 205-230. https://doi.org/10.1016/0022-247X(79)90189-6
  • A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy sets and systems 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  • D. Gopal and C. Vetro, Some new fixed point theorems in fuzzy metric spaces, Iranian Journal of Fuzzy Systems 11 (2014), 95-107.
  • M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy sets and Systems 27 (1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
  • V. Gregori, S. Morillas and A. Sapena, Examples of fuzzy metrics and applications, Fuzzy Sets and Systems 170 (2011), 95-111. https://doi.org/10.1016/j.fss.2010.10.019
  • V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9
  • M. Imdad, A. R. Khan, H. N. Saleh and W. M. Alfaqih, Some ϕ-fixed point results for (F,ϕ,α-ψ)-contractive type mappings with applications,...
  • M. Imdad, H. Saleh and W. Alfaqih, ϕ-best proximity point theorems in metric spaces with applications in partial metric spaces, TWMS J. of...
  • M. Jleli, B. Samet and C. Vetro, Fixed point theory in partial metric spaces via φ-fixed point's concept in metric spaces, Journal of...
  • O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy sets and Systems 12 (1984), 215-229. https://doi.org/10.1016/0165-0114(84)90069-1
  • I. Kramosil and J. Mich{'a}lek, Fuzzy metrics and statistical metric spaces, Kybernetika 11 (1975), 336-344.
  • P. Kumrod and W. Sintunavarat, A new contractive condition approach to φ-fixed point results in metric spaces and its applications, Journal...
  • P. Kumrod and W. Sintunavarat, On generalized Ri's contraction mappings and its applications, Computational and Applied Mathematics 37...
  • P. Kumrod and W. Sintunavarat, On new fixed point results in various distance spaces via φ-fixed point theorems in d-generalized metric spaces...
  • D. Miheţ, On fuzzy epsilon-contractive mappings in fuzzy metric spaces, Fixed Point Theory and Applications 2007 (2007), p. 87471. https://doi.org/10.1155/2007/87471
  • D. Miheţ, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159 (2008), 739-744. https://doi.org/10.1016/j.fss.2007.07.006
  • H. Saleh, M. Imdad and W. Alfaqih, Some metrical ϕ-fixed point results of Wardowski type with applications to integral equations, Bol. Soc....
  • H. N. Saleh, I. A. Khan, M. Imdad and W. M. Alfaqih, New fuzzy φ-fixed point results employing a new class of fuzzy contractive mappings,...
  • B. Samet, C. Vetro and P. Vetro, Fixed point theorems for alpha-psi-contractive type mappings, Nonlinear Analysis: Theory, Methods & Applications...
  • M. Sangurlu and D. Turkoglu, Fixed point theorems for (ψ-φ)-contractions in a fuzzy metric spaces, Journal of Nonlinear Sciences and Applications...
  • B. Schweizer and Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334. https://doi.org/10.2140/pjm.1960.10.313
  • S. Sedghi, N. Shobkolaei and I. Altun, A new approach to Caristi's fixed point theorem on non-Archimedean fuzzy metric spaces, Iranian...
  • S. Sedghi, N. Shobkolaei, T. Došenović and S. Radenović, Suzuki-type of common fixed point theorems in fuzzy metric spaces, Mathematica Slovaca...
  • M. S. Sezen and D. Türkoğlu, Some fixed point theorems of (F,ϕ)-fuzzy contractions in fuzzy metric spaces, Journal of Inequalities & Special...
  • P. Tirado, On compactness and G-completeness in fuzzy metric spaces, Iranian Journal of Fuzzy Systems 9 (2012), 151-158.
  • C. Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 162 (2011), 84-90. https://doi.org/10.1016/j.fss.2010.09.018
  • H. Vu, Existence results for fuzzy Volterra integral equation, Journal of Intelligent & Fuzzy Systems 33 (2017), 207-213. https://doi.org/10.3233/JIFS-161467