FUZZY QUASI-METRIC VERSIONS OF A THEOREM OF GREGORI AND SAPENA

Document Type : Research Paper

Author

Department of Mathematics, West University of Timisoara, Bv. V. Parvan 4, Timisoara, Romania

Abstract

We provide fuzzy quasi-metric versions of a fixed point theorem of
Gregori and Sapena for fuzzy contractive mappings in G-complete fuzzy metric
spaces and apply the results to obtain fixed points for contractive mappings
in the domain of words.

Keywords


[1] P. Flajolet, Analytic analysis of algorithms, in Lecture Notes in Computer Science, Springer,
Berlin, 623 (1992), 186-210.
[2] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1983), 385-389.
[3] M. Grabiec, Y. J. Cho and V. Radu, On nonsymmetric topological and probabilistic structures,
New York, Nova Science Publishers, Inc., 2006.
[4] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
64 (1994), 395-399.
[5] V. Gregori and A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and
Systems, 125 (2002), 245-252.
[6] V. Gregori and S. Romaguera, Fuzzy quasi-metric spaces, Appl. Gen. Topology, 5 (2004),
129-136.
[7] O. HadĖ‡zi´c and E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic
Publishers, Dordrecht, 2001.
[8] O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11
(1975), 336-344.
[9] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,
144 (2004), 431-439.
[10] D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems,
158 (2007), 915-921.
[11] M. Rafi and M. S. M. Noorani, Fixed point theorem in intuitionistic fuzzy metric spaces,
Iranian Journal of Fuzzy Systems, 3(1) (2006), 23-29.
[12] A. Razani and M. Shirdaryazdi, Erratum to:” On fixed point theorems of Gregori and
Sapena”, Fuzzy Sets and Systems, 153(2) (2005), 301-302.
[13] A. Razani, A contraction theorem in fuzzy metric spaces, Fixed Point Theory Applications,
3 (2005), 257-265.
[14] S. Romaguera, A. Sapena and P. Tirado, The banach fixed point theorem in fuzzy quasi-metric
spaces with application to the domain of words, Topology and its Applications, 154(10)
(2007), 2196-2203.
[15] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for  -weakly commuting
maps in L-fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1) (2008), 47-54.
[16] B. Schweizer and A. Sklar, Probabilistic metric spaces, North-Holland, Amsterdam, 1983.
[17] R.Vasuki and P. Veeramani, Fixed point theorems and Cauchy sequences in fuzzy metric
spaces, Fuzzy Sets and Systems, 135 (2003), 415-417.
[18] T. Zikic, On fixed point theorems of Gregori and Sapena, Fuzzy Sets and Systems, 144(3)
(2004), 421-429.