EXTENSIONS OF BANACH'S AND KANNAN'S RESULTS IN FUZZY METRIC SPACES

Title & Authors
EXTENSIONS OF BANACH'S AND KANNAN'S RESULTS IN FUZZY METRIC SPACES
Choudhur, Binayak S.; Das, Krishnapada; Das, Pradyut;

Abstract
In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.
Keywords
Hadzic type t-norm;fuzzy metric space;Cauchy sequence;$\small{{\Psi}}$-function;weakly compatible mappings;contraction principle;Kannan type mapping;coincidence point;fixed point;
Language
English
Cited by
1.
Coupled coincidence point results in partially ordered generalized fuzzy metric spaces with applications to integral equations, Mathematical Sciences, 2016, 10, 1-2, 23
References
1.
V. Berinde, Picard iteration converges faster than Mann iteration for a class of quasi contractive operators, Fixed Point Theory Appl. 2004 (2004), no. 2, 97-105.

2.
B. S. Choudhury and K. Das, Fixed points of generalized Kannan type mappings in generalized Menger spaces, Commun. Korean Math. Soc. 24 (2009), no. 4, 529-537.

3.
B. S. Choudhury and P. N. Dutta, Fixed point result for a sequence of mutually con- tractive self-mappings on fuzzy metric spaces, J. Fuzzy Math. 13 (2005), no. 3, 723-730.

4.
B. S. Choudhury and A. Kundu, A common fixed point result in fuzzy metric spaces using altering distances, J. Fuzzy Math. 18 (2010), no. 2, 517-526.

5.
L. Ciric, Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces, Chaos Solitons Fractals 42 (2009), no. 1, 146-154.

6.
E. H. Connell, Properties of fixed point spaces, Proc. Amer. Math. Soc. 10 (1959), 974-979.

7.
A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), no. 3, 395-399.

8.
A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems 90 (1997), no. 3, 365-368.

9.
M. Grabice, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988), no. 3, 385-389.

10.
V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), no. 2, 245-253.

11.
F. Gu, Strong convergence of an explicit iterative process with mean errors for a finite family of Ciric quasi contractive operators in normed spaces, Math. Commun. 12 (2007), no. 1, 75-82.

12.
O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Space, Kluwer Academic Publishers, Dordrecht, 2001.

13.
G. Jungck and B. E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), no. 3, 227-238.

14.
R. Kannan, Some results on fixed point, Bull. Calcutta Math. Soc. 60 (1968), 71-76.

15.
R. Kannan, Some results on fixed point, Amer. Math. Monthly 76 (1969), 405-408.

16.
I. Kramosil and J. Michaiek, Fuzzy metric and statistical metric spaces, Kybernetika (Prague) 11 (1975), no. 5, 336-344.

17.
D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems 144 (2004), no. 3, 431-439.

18.
D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems 158 (2007), no. 8, 915-921.

19.
A. Razani, A contraction theorem in fuzzy metric spaces, Fixed Point Theory Appl. 2005 (2005), no. 3, 257-265.

20.
J. Rodriguez Lopez and S. Ramaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems 147 (2004), no. 2, 273-283.

21.
N. Shioji, T. Suzuki, and W. Takahashi, Contractive mappings, Kannan mappings and metric completeness, Proc. Amer. Math. Soc. 126 (1998), no. 10, 3117-3124.

22.
P. V. Subrahmanyam, Completeness and fixed points, Monatsh. Math. 80 (1975), no. 4, 325-330.

23.
R. Vasuki, A common fixed point theorem in a fuzzy metric space, Fuzzy Sets and Systems 97 (1998), no. 3, 395-397.

24.
L. A. Zadeh, Fuzzy sets, Information and control 8 (1965), 338-353.