Estimation of fuzzy metric spaces from ordinary metric spaces

Authors

  • P Senthil Kumar BHARATHIDASAN UNIVERSITY,THIRUCHIRAPALLI
  • Thiruveni Packirisamy BHARATHIDASAN UNIVERSITY.THIRUCHIRAPALLI

DOI:

https://doi.org/10.23755/rm.v41i0.670

Keywords:

ordinary metric space, fuzzy functional analysis, fixed point theorem

Abstract

In this paper we estimate the new way for analyzing the fuzzy metric spaces from ordinary metric spaces using fuzzy fixed point theorem and vice versa. We derive some definitions and theorems for analyzing the metric spaces with new structure of fuzzy metric space using  fixed point theorems. Also we have given new examples for fuzzy metric spaces using   fixed point theorem.

Author Biographies

  • P Senthil Kumar, BHARATHIDASAN UNIVERSITY,THIRUCHIRAPALLI
    MATHEMATICS
  • Thiruveni Packirisamy, BHARATHIDASAN UNIVERSITY.THIRUCHIRAPALLI
    MATHEMATICS

References

Saleh Omran, H.S. Al-Saadi (2017), some notes on metric and fuzzy metric spaces. International Journal Of Advanced and Applied Sciences, 4(5) 2017, Pages: 41-43

Fréchet MM (1906). Surquelques points du calcul fonctionnel. Rendicontidel Circolo Matematico di Palermo (1884-1940), 22(1): 1-72.

George A and Veeramani P (1994). On some results of fuzzy metric spaces. Fuzzy Sets and Systems, 64(3):395-399.

Erceg M A(1979). Metric spaces in fuzzy set theory. Journal of Mathematical Analysis and Applications, 69(1):205-230.

Mihet D (2004). A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets and Systems, 144(3):431-439.

Valentin Gregori, Samuel Morillas, Almanzor Sapena,(2011) Examples of fuzzy metrics and applications, Fuzzy Sets and Systems 170, 95-111.

Diamond P and Kloden P (1999). Metric space so fuzzy sets. Fuzzy Sets and Systems, 35(2):241-249.

Schweizer B and Skala A (1960), Statistical metric spaces. The Pacific Journal of Mathematics, 10(1):314-334.

Dhamodharan D, Nihal Tas and Krishnakumar R (2019), Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application, Mathematical Sciences and Applications E-Notes, 7 (1), 9-18.

Zadeh LA (1965), Fuzzy sets. Information and Control, 8(3): 338-353.

Gregori V and Romaguera S (2000), Some properties of fuzzy metric spaces. Fuzzy Sets and Systems, 115(3):485-489.

Shen Y, Qiu D, and Chen W (2012), Fixed point theorems in fuzzy metric spaces. Applied Mathematics Letters, 25(2):138-141.

George A and Veeramani P (1997), On Some Results of Analysis For Fuzzy Metric Spaces; Fuzzy Sets and Systems (90) 365-368.

Karmosil O, Michalek J (1975) Fuzzy metric and Statistical Metric Spaces, Kybernetica 11 326-334.

Banach S (1922), sur les operations dans les ensembles abstraits etleur application aux equations integrals. Fundamenta Mathematicae, Vol.3, pp.133-181

Krishnakumar R, Damodharan D (2016), Fixed point theorems in normal cone metric spaces, International Journal of Math.Sci & Engg.appls.10, 213-224.

Downloads

Published

2021-12-31

Issue

Section

Volume 41-2021