Banach's and Kannan's fixed point results in fuzzy 2metric spaces
DOI:
https://doi.org/10.4067/S071609172013000400005Keywords:
Fuzzy 2metric space, Hadzic type tnorm, Weakly compatible mapping, ψfunction.Abstract
In this paper we establish two common fixed point theorems in fuzzy 2metric spaces. These theorems are generalizations of the Banach Contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy 2metric spaces.References
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[2] B. S Choudhury K.Das and P.Das, Extensions of Banach’s and Kannan’s results in Fuzzy metric Space. Hacettepe Journal of Mathematics and Statistics, 39(1), pp. 19, (2009).
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[8] O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Space, Kluwer Academic Publishers, Dordrecht, (2001).
[9] S. Heipern, Fuzzy mapping and fixed point theorems, J. Maths, Anal. Appl. 83, pp. 565569, (1981).
[10] O. Kramosil and J. Michalek: Fuzzy metric and statistical metric spaces, Kybernelika, 11, pp. 326334, (1975).
[11] B. C. Tripathy and A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50(4), pp. 565574, (2010).
[12] B. C. Tripathy and A. Baruah, M.Et and M. Gungor, On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers, Iranian Jour. Sci. Tech., Trans. A : Sci., 36 (2), pp. 147155, (2012).
[13] B. C. Tripathy and S. Borgogain, Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function; Adv. Fuzzy Syst., 2011, Article ID216414, 6 pages (2011).
[14] B. C. Tripathy and A. J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers, Jour. Intell. Fuzzy Syst., 24 (1), pp. 185189, (2013).
[15] B. C. Tripathy and S. Debnath, γopen sets and γcontinuous mappings in fuzzy bitopological spaces, Jour. Intell. Fuzzy Syst., 24(3), pp. 631635, (2013).
[16] B. C. Tripathy and G.C. Ray, On Mixed fuzzy topological spaces and countability, Soft Comput., 16 (10), pp. 16911695, (2012).
[17] B. C. Tripathy and B. Sarma, On Iconvergent double sequences of fuzzy real numbers; Kyungpook Math. J., 52 (2), pp. 189200, (2012).
[18] S. Sharma, On fuzzy metric space, Southeast Asian Bulletin of Mathematics, 26, pp. 133145, (2002).
[2] B. S Choudhury K.Das and P.Das, Extensions of Banach’s and Kannan’s results in Fuzzy metric Space. Hacettepe Journal of Mathematics and Statistics, 39(1), pp. 19, (2009).
[3] B. S. Choudhury and A. Kundu, A common fixed point result in fuzzy metric spaces using altering distances, J. Fuzzy Math. 18 (2), pp. 517 52, (2010).
[4] L. Ciric, Some new results for Banach contradiction and Edelstein contractive mappings on fuzzy metric spaces, chaos solitons fractals 42(1), pp. 146154, (2009).
[5] S. Gahler, Linear 2normierte Raume, Math. Nachr, 28 pp. 143, (1964).
[6] S. Gahler, U ber 2Banach Raume, Math. Nachr. 42, pp. 335347, (1969).
[7] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy sets and systems 64(3), pp. 395399, (1994).
[8] O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Space, Kluwer Academic Publishers, Dordrecht, (2001).
[9] S. Heipern, Fuzzy mapping and fixed point theorems, J. Maths, Anal. Appl. 83, pp. 565569, (1981).
[10] O. Kramosil and J. Michalek: Fuzzy metric and statistical metric spaces, Kybernelika, 11, pp. 326334, (1975).
[11] B. C. Tripathy and A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50(4), pp. 565574, (2010).
[12] B. C. Tripathy and A. Baruah, M.Et and M. Gungor, On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers, Iranian Jour. Sci. Tech., Trans. A : Sci., 36 (2), pp. 147155, (2012).
[13] B. C. Tripathy and S. Borgogain, Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function; Adv. Fuzzy Syst., 2011, Article ID216414, 6 pages (2011).
[14] B. C. Tripathy and A. J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers, Jour. Intell. Fuzzy Syst., 24 (1), pp. 185189, (2013).
[15] B. C. Tripathy and S. Debnath, γopen sets and γcontinuous mappings in fuzzy bitopological spaces, Jour. Intell. Fuzzy Syst., 24(3), pp. 631635, (2013).
[16] B. C. Tripathy and G.C. Ray, On Mixed fuzzy topological spaces and countability, Soft Comput., 16 (10), pp. 16911695, (2012).
[17] B. C. Tripathy and B. Sarma, On Iconvergent double sequences of fuzzy real numbers; Kyungpook Math. J., 52 (2), pp. 189200, (2012).
[18] S. Sharma, On fuzzy metric space, Southeast Asian Bulletin of Mathematics, 26, pp. 133145, (2002).
How to Cite
[1]
B. Chandra Tripathy, S. Paul, and N. Ram Das, “Banach’s and Kannan’s fixed point results in fuzzy 2metric spaces”, Proyecciones (Antofagasta, On line), vol. 32, no. 4, pp. 359375, 1.
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