### Some Fixed Point Theorems in Generalized M-Fuzzy Metric Space

#### Abstract

In this paper, some fixed point theorems in Generalized (G) metric space have been converted using Generalized M (GM)-fuzzy metric space. In Paper [8], the expansive mapping has been defined using generalized metric space. Here, at first the expansive mapping has been defined using generalized M-fuzzy metric space and later generalized some lemma’s from generalized metric space to Generalized-M fuzzy metric space. Using these lemma’s and the new definition of expansive mapping the generalized fixed point theorems are proved under some contractive conditions.

#### Keywords

#### Full Text:

PDF#### References

A. Deb Ray and P.K. Saha, Fixed point theorems on Generalized Fuzzy Metric spaces, Hacettepe Jour. Math. Statistics, 39(1) (2010), 1-9.

B.C. Dhange, Generalized metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc., 84(4)(1992) 329-336

A. George, and P. Veeramani, On some results in fuzzy metric space Fuzzy Sets Syst., 64(3) (1994), 395-399.

O. Kramosil, and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernelika. 11 (1975), 326-334.

Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorem for Mapping on complete G-metric spaces, Fixed Point Theory Appl., 2008(2008) article ID 189870, doi: 10.1155/2008/189870

Z. Mustafa, A new structure for generalized metric spaces - with application to fixed point theory, Ph.D. Thesis, the University of New Castle, Australia, 2005.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Jour. Nonlinear Conv. Anal., 7(2) (2006), 289-297

Z. Mustafa, F. Awawdeh and W. Shatanawi, Fixed point theorem for expansive mapping in G-metric spaces, Int. J. Contemp. Math, Sci., 5(50)(2010), 2463-2472.

S. Sedghi, N. Shobe and H. Zhou, A common fixed point theorem in D*-metric spaces, Fixed Point Theory Appl., 2007(2007) Article ID 27906, 1-13

G.P. Sun and K. Yang, Generalized fuzzy metric spaces with Properties, Research Journal of Applied Sciences, Engineering and Technology, 2(7) (2010) 673-678.

B.C. Tripathy and S. Borgogain, Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function, Advances in Fuzzy Systems, 2011), Article ID216414, 6 pages.

B.C. Tripathy and A. J. Dutta, On I-acceleration convergence of sequences of fuzzy real numbers, Math. Modell. Analysis, 17(4) (2012), 549-557.

B.C. Tripathy, S. Paul and N.R. Das Banach’s and Kannan’s fixed point results in fuzzy 2-metric spaces, Proyecciones J. Math., 32(4)(2013),359-375.

B.C. Tripathy, S. Paul and N.R. Das, A fixed point theorem in a generalized fuzzy metric space, Boletim da Sociedade Paranaense de Matematica, 32(2) (2014), 221-227.

B.C. Tripathy, S. Paul and N.R. Das Fixed point and periodic pint theorems in fuzzy metric space, Songklanakarin Journal of Science and Technology, 37(1) (2015), 89-92.

B.C. Tripathy and G.C. Ray On mixed fuzzy topological spaces and countability, Soft Computing, 16(10)(2012), 1691-1695

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution 3.0 License.