Generalized contraction theorem in M -fuzzy cone metric spaces

Main Article Content

Mookiah Suganthi
Mathuraiveeran Jeyaraman
Avulichikkanan Ramachandran

Abstract

This work defines MM-Fuzzy Cone Metric Space, as a new metric space. It also analyzes possible forms of contractive conditions and groups them accordingly to set up generalized contractive conditions for self-mappings defined over MM-fuzzy cone metric spaces. We prove the existence of fixed points of these mappings and exhibit the same through a suitable example.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Article Details

How to Cite
[1]
Suganthi, M., Jeyaraman, M. and Ramachandran, A. 2022. Generalized contraction theorem in M -fuzzy cone metric spaces. Journal of Innovative Applied Mathematics and Computational Sciences. 2, 3 (Dec. 2022), 29–40. DOI:https://doi.org/10.58205/jiamcs.v2i3.48.
Section
Research Articles
Author Biography

Mathuraiveeran Jeyaraman, PG and Research Department of Mathematics

 

 

 

References

S. Banach, Sur les operations dans les ensembles abstraits et leur application aux équations integrales, Fund. Math., 3 (1922), 133-181.

Z. Deng, Fuzzy pseudo-metric spaces, J. Math. Anal. Appl., 86(1) (1982), 74-95.

P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 35(2)(1990), 241-249.

M. A. Erceg, Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69(1) (1979), 205-230.

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

A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90(3)(1997), 365-368.

V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy sets and Systems, 125 (2002), 245-252.

V. Gupta, S. S. Chauhan and I. K. Sandhu, Banach Contraction Theorem on Extended Fuzzy Cone b-metric Space, Thai J. Math., 20(1)(2022), 177-194.

V. Gupta, A. Kaushik and M. Verma, Some new fixed point results on $V-psi$-fuzzy contraction endowed with graph, Journal of Intelligent & Fuzzy Systems, 36(6) (2019), 6549-6554.

G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16(2) (1973), 201-206.

L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contraction mappings, J. Math. Anal. Appl., 332(2) (2007), 1468-1476.

O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12(3) (1984), 215-229.

I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11(5) (1975), 326-334.

T. O¨ ner, M. B. Kandemir and B. Tanay, Fuzzy cone metric spaces, J. Nonlinear Sci. Appl., 5 (2015), 610-616.

U. R. Saif and L. Hong-Xu, Fixed point theorems in fuzzy cone metric spaces, J. Nonlinear Sci. Appl., 10 (2017), 5763-5769.

S. Sedghi and N. Shobe, Fixed point theorem in M-fuzzy metric spaces with property (E), Advances in Fuzzy Mathematics, 1(1) (2006), 55-65.

T. Turkoglu and M. Abuloha, Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Math. Sin. (Engl. Ser.), 26 (2010), 489-496.

C. S. Wong, Generalized contractions and fixed point theorems, Proc. Amer. Math. Soc., 42(2) (1974), 409-417. DOI

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