Common coupled fixed point theorems in fuzzy metric spaces

K.P.R. RAO, K.R.K. RAO, Shaban SEDGHI
2.015 446

Abstract


In this paper , we obtain two general common coupled fixed point theorems  for  maps in fuzzy metric spaces.

Keywords


Fuzzy metric space,common fixed points, weakly compatible maps , Coupled fixed point

Full Text:

PDF

References


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

B. Schweizer and A. Sklar,Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334.

B. Singh and M. S. Chauhan, Common fixed points of compatible maps in fuzzy metric spaces, Fuzzy Sets Syst., 115 (2000), 471-475.

B. Singh and S. Jain, Semi compatibility and fixed point theorems in fuzzy metric space using implicit relation, Internat. J. Math. Math. Sci., 16 (2005), 2617-2629.

B.Singh and S. Jain, Semi mpatibility,compatibility and fixed point theorems in fuzzy metric space, J. Chung Cheong Math. Soc., 18 (1) (2005),1-22.

C. Alaca, Fixed point results for mappings satisfying a general contractive condition of operator type in dislocated fuzzy quasi-metric spaces, J. Comput. Anal. Appl., 12, (1-b) (2010), 361-368.

C. Alaca, D. Turkoglu and C. Yildiz, Fixed Points in Intuitionistic Fuzzy Metric Spaces, Chaos, Solitons & Fractals, 29, (5) (2006), 1073-1078.

D. Turkoglu, C. Alaca, Y. J. Cho and C. Yildiz, Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces, J. Appl. Math. Comput., 22, (1-2) (2006), 411-424.

D.Turkoglu, I. Altun and B. Fisher, Common fixed point theorems for four mappings with some weak conditions of commutativity, Novi Sad J. Math., 36, (1) (2006), 75-86.

I. Altun and D. Turkoglu, Fixed points of sequences of maps on fuzzy metric spaces. Ital. J. Pure Appl. Math, 24, (27) (2008), 27 - 34.

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

J. Rodríguez López, S. Ramaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets Sys,147 (2004), 273-283.

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

M.Abbas,M.Alikhan and S.Radenovic, Common coupled fixed point theorems in cone metric spaces for W-compatible mappings, Applied Mathematics and Computation, 217, (1) (2010), 195 – 202.

M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst., 27 (1988), 385-389.

O. Hadzic and E. Pap, A fixed point theorem for multi valued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets Syst., 127 (2002), 333-344.

R.Chugh and S.Kumar, Common fixed point theorems in fuzzy metric spaces, Bull. Cal. Math. Soc., 94 (1) (2002), 17-22.

R. Saadati, A. Razani, and H. Adibi, A common fixed point theorem in -fuzzy metric spaces, Chaos, Solitons and Fractals, Chaos. (2006), 01- 023.

R. Vasuki, Common fixed points for R-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math., 30 (1999), 419-423.

S. N. Mishra, S. N. Sharma and S. L. Singh, Common fixed points of maps in fuzzy metric spaces, Internat. J. Math. Math. Sci., 17 (1994), 253-258.

S. Sharma, Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets Syst., 127 (2002), 345- 352.

Shaban Sedghi,Ishak Altun and Nabi Shobe,Coupled

fixed point theorems for contractions in fuzzy metric

spaces, Nonlinear Analysis,72(2010),1298-1304.

T.G.Bhaskar and V.Lakshmikantham, Fixed point theorems in partially ordered cone metric spaces and applications, Nonlinear Analysis: Theory, methods and Applications, 65, (7) (2006), 825-832.

Xin-Qi Hu , Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces, Fixed point theory and Applications, 2011, Article ID 363716, 14 pages, doi: 10.1155/2011/363716.

Y.J.Cho, Fixed points in fuzzy metric spaces,

J. Fuzzy Math., 5 (1997), 949-962.

Y. J. Cho, H. K. Pathak, S. M. Kang and J. S. Jung, Common fixed points of compatible maps of type ( ) (1998), 99-111.