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Quasi-contractive Mappings in Fuzzy Metric Spaces | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 12، شماره 4، آبان 2015، صفحه 147-153 اصل مقاله (284.26 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2015.2090 | ||
| نویسندگان | ||
| A. Amini-Harandi1؛ D. Mihet* 2 | ||
| 1Department of Mathematics, University of Isfahan, Isfahan, 81745- 163, Iran | ||
| 2West University of Timisoara, Faculty of Mathematics and Computer Science, Bv. V. Parvan 4, 300223, Timisoara, Romania | ||
| چکیده | ||
| We consider the concept of fuzzy quasi-contractions initiated by '{C}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{H}$-contractive mappings on M-complete fuzzy metric spaces in the sense of George and Veeramani.The results are illustrated by a representative example. | ||
| کلیدواژهها | ||
| Fuzzy metric space؛ Fuzzy quasi-contractive mapping؛ Fixed point | ||
| مراجع | ||
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[1] Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45(2) (1974), 267-273. [2] S. Chang, Y. J. Cho and S. M. Kang, Probabilistic Metric Spaces and Nonlinear Operator Theory, Sichuan Univ. Press, 1994. [3] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64(3) (1994), 395-399. [4] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(3) (1988), 385-389. [5] V. Gregori and A. Sapena, On xed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125(2) (2002), 245-252. [6] O. Hadzic and E. Pap, Fixed point theory in probabilistic metric spaces, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, Boston, London, 536 (2001). [7] F. Kiany and A. Amini-Harandi, Fixed points and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces, Point Theory and Applications 2011, 2011:94. [8] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Trends in Logics, Kluwer Academic Publishers, Dordrecht, Boston, London, 8 (2000). [9] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5) (1975), 336-344. [10] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, 144(3) (2004), 431-439. [11] D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems, 158(8) (2007), 915-921. [12] D. Mihet, Fuzzy -contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159(6) (2008), 739-744. [13] D. Mihet, A note on fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems, 251 (2014), 83-91. [14] J. Rodrguez-Lopez and S. Romaguera, The Hausdor fuzzy metric on compact sets, Fuzzy Sets and Systems, 147(2) (2004), 273-283. [15] B. Schweizer and A. Sklar, Statistical metric spaces, Paci c J. Math., 10 (1960), 313-334. [16] C. Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 162(1) (2011), 84-90. [17] D. Wardowski, Fuzzy contractive mappings and xed points in fuzzy metric spaces, Fuzzy Sets and Systems, 222 (2013), 108-114. | ||
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