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

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.