Vaezpour, S., Vaezzadeh, S. (2015). Generalized Weakly Contractions in Partially Ordered Fuzzy Metric Spaces. Iranian Journal of Fuzzy Systems, 12(1), 123-129. doi: 10.22111/ijfs.2015.1866

S. M. Vaezpour; S. Vaezzadeh. "Generalized Weakly Contractions in Partially Ordered Fuzzy Metric Spaces". Iranian Journal of Fuzzy Systems, 12, 1, 2015, 123-129. doi: 10.22111/ijfs.2015.1866

Vaezpour, S., Vaezzadeh, S. (2015). 'Generalized Weakly Contractions in Partially Ordered Fuzzy Metric Spaces', Iranian Journal of Fuzzy Systems, 12(1), pp. 123-129. doi: 10.22111/ijfs.2015.1866

Vaezpour, S., Vaezzadeh, S. Generalized Weakly Contractions in Partially Ordered Fuzzy Metric Spaces. Iranian Journal of Fuzzy Systems, 2015; 12(1): 123-129. doi: 10.22111/ijfs.2015.1866

Generalized Weakly Contractions in Partially Ordered Fuzzy Metric Spaces

^{1}Department of Mathematics and Computer Science, Amirkabir Uni- versity of Technology, 424 Hafez Avenue, Tehran 15914, Iran

^{2}Department of Mathematics and Computer Science,, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran

Abstract

In this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and coincidence point theorems on partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.

[1] M. A. Ahmed, Fixed point theorems in fuzzy metric spaces, Journal of the Egyptian Mathe- matical Society, (in press). [2] Y. J. Cho, Fixed points in fuzzy metric spaces. J Fuzzy Math, 39 (1997), 949-962. [3] Y. J. Cho, S. Sedghi, N. Shobe, Generalized xed point theorems for compatible mappings with some types in fuzzy metric spaces. J Fuzzy Math, 39 (2009), 2233-2244. [4] L. B. Ciric, D. Mihet and R. Saadati, Monotone generalized contractions in partially ordered probabilistic metric spaces, Topol. Appl., 156 (2009), 2838-2844. [5] M. Goudarzi and S. M. Vaezpour,On the denition of fuzzy Hilbert spaces and its application, J. Nonlinear Sci. Appl., 2(1) (2009) 46-59. [6] O. Hadzic and E. Pap, Fixed Point Theory in PM Spaces, Kluwer Academic Publ., 2001. [7] Y. Liu and Z. Li, Coincidence point theorems in probabilistic and fuzzy metric spaces, 158 (2007), 58-70. [8] D. Mihe t, A generalization of a contraction principle in probabilistic metric spaces (II), Int. J. Math. Math. Sci, 5 (2005), 729-736. [9] S. N. Mishra, N. Sharma and S. L. Singh, Common xed points of maps on fuzzy metric spaces, International Journal of Mathematics and Mathematical Sciences, 17 (1994), 253- 258. [10] S. H. Nasseri, Fuzzy nonlinear optimization, Nonlinear Anal, 1 (2008), 236-240. [11] H. K. Nashine and B. Samet, Fixed point results for mappings satisfying ( ; ') weakly contractive condition in partially ordered metric spaces, Nonlinear Anal, 74 (2011), 2201- 2209. [12] D. O'Regan and R. Saadati, Nonlinear contraction theorems in probabilistic spaces. Appl. Math. Comput, 195 (2008), 86-93. [13] B. Singh and M. S. Chauhan, Common xed points of compatible maps in fuzzy metric spaces, Fuzzy Sets and Systems, 115 (2000), 471-475. [14] B. Singh and S. Jain, Semi-compatibility, compatibility and xed point theorems in Fuzzy metric space, Journal of Chungecheong Math. Soc., 18(1) (2005), 1-22. [15] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier North Holand, New York, 1983. [16] P. V. Subrahmanyam, A Common xed point theorem in fuzzy metric spaces, Information Sciences, 83 (1995), 109-112