A COMMON FIXED POINT THEOREM FOR SIX WEAKLY COMPATIBLE MAPPINGS IN M-FUZZY METRIC SPACES

Document Type : Research Paper

Authors

1 Department of Mathematics, Islamic Azad University-Ghaemshahr Branch, Ghaemshahr P.O.Box 163, Iran

2 Department of Applied Mathematics, Acharya Nagarjuna University- Nuzvid Campus, Nuzvid-521201, A.P., India

3 Department of Mathematics, Islamic Azad University-Babol Branch, Iran

Abstract

In this paper, we give some new definitions of M-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete M-fuzzy metric spaces.

Keywords


[1] J. C. Chang, H. Chen, S. M. Shyu and W. C. Lian, Fixed point theorems in fuzzy real line,
Computers and Mathematics with Applications,47(2004), 845-851.
[2] Z. K. Deng,Fuzzy pseudo-metric spaces, J. Math. Anal. Appl., 86 (1982), 74-95.
[3] B. C. Dhage,A common fixed point principe in D-metric spaces, Bull. Calcutta Math. Soc.,
91(1999), 475-480.
[4] B. C. Dhage, A. M. Pathan and B. E. Rhoades,A general existence priciple for fixed point
theorem in D-metric spaces, Int. J. Math. Math. Sci., 23 (2000), 441-448.
[5] B. C. Dhage,Generalised metric spaces and mappings with fixed point, Bull. Calcutta Math.
Soc.,84(4) (1992), 329-336.
[6] M. S. El Naschie,A review of E-infinity theory and the mass spectrum of high energy particle
physics, Chaos, Solitons and Fractals, 19 (2004), 209-236.
[7] M. S. El Naschie,On a fuzzy Kahler-like Manifold which is consistent with two-slit experiment,
Int. J. of Nonlinear Science and Numerical Simulation,6 (2005), 95-98.
[8] M. S. El Naschie,On the uncertainty of Cantorian geometry and two-slit experiment, Chaos,
Solitons and Fractals,9 (1998), 517-529.
[9] M. S. El Naschie,The idealized quantum two-slit gedanken experiment revisited-Criticism
and reinterpretation, Chaos, Solitons and Fractals, 27 (2006), 9-13.
[10] M. A. Erceg,Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69 (1979), 205-230.
[11] J. X. Fang,On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 46
(1992), 107-113.
[12] M. Grabiec,Fixed point in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.
[13] V. Gregori and A. Sapena,On fixed-point theorem in fuzzy metric spaces, Fuzzy Sets and
Systems,125 (2002), 245-252.
[14] A. George and P. Veeramani,On some result in fuzzy metric space, Fuzzy Sets and Systems,
64(1994), 395-399.
 
[15] V. Gregori, S. Romaguera and P. Veeramani,A note on intuitionistic fuzzy metric spaces,
Chaos , Solitons and Fractals,28(2006), 902-905.
[16] V. Gregori and S. Romaguera,Some proerties of fuzzy metric spaces, Fuzzy Sets and Systems,
115(2000), 485-489.
[17] O. Hadzic and E. Pap,Fixed Point Theory in Probabilistic Metric Spaces, Mathematics and
Its Applications, Vol. 536, Kluwer Academic Publishers, Dordrecht, 2001.
 
[18] O. Hadzic,Fixed point theorems in probabilistic metric spaces, Serbian Academy of Sciences
and Arts, Institute of Mathematics, University of Novi Sad, Yugoslavia, 1995.
 
[19] O. Kaleva and S. Seikkala,On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
215-229.
 
[20] I. Kramosil and J. Michalek,Fuzzy metric and statistical metric spaces, Kybernetica, 11
(1975), 326-334.
 
[21] V. Lakshmikantham and A. S. Vatsala,Existence offixed points of fuzzy mappings via theory
of fuzzy differential equations, Journal of Computational and Applied Mathematics, 113
(2000), 195-200.
 
[22] D. Mihet¸,A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,
144(2004), 431-439.
[23] S. V. R. Naidu, K. P. R. Rao and N. Srinivasa Rao,On convergent sequences and fixed point
theorems in D-Metric spaces, Internat. J. Math. Math. Sci. 2005, 12 (2005), 1969-1988.
[24] S. V. R. Naidu, K. P. R. Rao and N. Srinivasa Rao,On the topology of D-metric spaces and
the generation of D-metric spaces from metric spaces, Internat. J. Math. Math. Sci.2004, 51
(2004), 2719-2740.
 
[25] J. J. Nieto and Rodriguez-Lopez,Existence of extremal solutions for quadratic fuzzy equations,
Fixed Point Theory and Applications,3(2005), 321-342.
[26] J. J. Nieto, R. L. Pouso and R. Rodriguez-Lopez,Fixed point theorems on ordered abstract
spaces, Proceedings of American Mathematical Society(in press).
[27] V. Radu,Lectures on Probabilistic Analysis, Surveys, Lecture Notes and Monographs.Series
on Probability, Statistics and Applied Mathematics, Vol. 2, Universitatea din Timisoara,
 
Timisoara, 1994.
 
[28] M. Rafi and M. S. M. Noorani,Fixed point theorem on Intuitionistic Fuzzy Metric spaces,
Iranian J. Fuzzy System,3 (2006), 23-29.
[29] J. Rodr´─▒guez L´opez and S. Ramaguera,The Hausdorff fuzzy metric on compact sets, Fuzzy
Sets and Systems,147 (2004), 273-283.
[30] R. Saadati and J. H. Park,On the intuitionistic fuzzy topological spaces, Chaos, Solitons and
Fractals,27 (2006), 331-344.
[31] B. Schweizer and A. Sklar,Probabilistic Metric Spaces, Elsevier, North Holand, New York,
1983.
 
[32] B. Schweizer and A. Sklar,Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334.
[33] B. Schweizer, H. Sherwood and R. M. Tardiff,Contractions on PM-space examples and
counterexamples, Stochastica, 1 (1988), 5-17.
[34] 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.
[35] G. Song,Comments on “A common fixed point theorem in a fuzzy metric spaces”, Fuzzy
Sets and Systems,135 (2003), 409-413.
[36] Y. Tanaka, Y. Mizno and T. Kado,Chaotic dynamics in Friedmann equation, Chaos, Solitons
and Fractals,24 (2005), 407-422.
[37] R. Vasuki and P. Veeramani,Fixed point theorems and Cauchy sequences in fuzzy metric
spaces, Fuzzy Sets and Systems, 135 (2003), 415-417.
[38] R. Vasuki,Common fixed points for R-weakly commuting maps in fuzzy metric spaces, Indian
J. Pure Appl. Math.,30 (1999), 419-423.
[39] L. A. Zadeh,Fuzzy sets, Inform and Control, 8 (1965), 338-353.