Some Fixed Point Theorems in Generalized M-Fuzzy Metric Space
In this paper, some fixed point theorems in Generalized (G) metric space have been converted using Generalized M (GM)-fuzzy metric space. In Paper , 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.
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
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.