Volume 9 | Number 2 | Year 2014 | Article Id. IJMTT-V9P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V9P511
This paper presents some common fixed point theorem for compatible type mapping in fuzzy metric space. Our result generalizes the result of I.Altun and D.Turkoglu [6].
[1] A. George and P. Veeramani, “On some results in Fuzzy metric spaces”, Fuzzy Sets and Systems, vol. 64, pp. 395-399, 1994.
[2] B. Singh and M. S. Chauhan, “Common fixed points of compatible maps in fuzzy metric spaces”, Fuzzy Sets and Systems, vol.115, pp. 471-475, 2000.
[3] B.E. Rhoades, “Contractive definitions and continuity”, Contemporary Math., vol.72, pp.233-245, 1988.
[4] D.Turkoglu and B.E.Rhoades, “A fixed fuzzy point for fuzzy mapping in complete metric spaces”, Math. Communication, vol.10 2, pp.115-121, 2005.
[5] G. Jungck, “Compatible mappings and common fixed points”, International J. Math. Math. Sci., vol. (2), pp.285-288, 1988.
[6] Ishak Altun et al., “Some fixed point theorem on Fuzzy metric space with implicit relation”, Commun Korean Math.Soc., vol.23, pp. 111-124,2008.
[7] I. Istratescu, “A fixed point theorem for mappings with a probabilistic contractive iterate”, Rev. Roumaire. Math. Pure Appl., vol.26, pp. 431-435, 1981.
[8] I. Kramosil and J. Michalek, “Fuzzy metric and statistical metric spaces”, Kybernetica, vol.11, pp.336-344, 1975.
[9] L. A. Zadeh, “Fuzzy sets, Inform. and Control”, vol. 8, pp.338-353, 1965.
[10] M. Edelstein, “On fixed and periodic points under contraction mappings”, J. London Math. Soc., vol. 37, pp.74-79, 1962.
[11] M. Grabiec, "Fixed points in fuzzy metric specs, Fuzzy Sets and Systems”, vol. 27, pp. 385-389, 1988.
[12] O. Hadzic, “Common fixed point theorems for families of mapping in complete metric space”,Math. Japon , vol.29, pp. 127-134, 1984.
[13] O.Kramosil and J.Michalek, “Fuzzy metric and statistical metric space”, Kyber-netika (Praha), vol.11, pp.326-334, 1975.
[14] R.Vauski, “Common fixed points for R-weakly commuting maps in fuzzy metric space”, Indian J. Pure Appl. Math, vol.30, pp.419-423, 1999.
[15] S. Kutukcu et al., “Common fixed point of compatible maps of type on fuzzy metric spaces”, Commun.Korean Math. Soc., vol.21, No.1, pp. 89-100, 2006.
[16] S. N. Mishra, N. Sharma, and S. L. Singh, “Common fixed points of maps on fuzzy metric spaces”, Internat. J. Math. Sci., vol.17, pp. 253-258, 1994.
[17] S.Sharma et al, “On compatible mappings satisfying an implicit relation in common fixed point consideration”, Tamkang J. Math. , vol.33, pp.245-252, 2002.
[18] V. Popa, “A general coincidence theorem for compatible multivalued mapping satisfying an implicit relalation”, Demons ratio Math., vol.33, pp.159-164, 2000.
[19] Y. J. Cho, S. Sedghi, and N. Shobe, “Generalized fixed point theorems for Compatible mappings with some types in fuzzy metric spaces”, Chaos, Solitons and Fractals, vol.39, pp.2233-2244, 2009.
[20] Y.J. Cho, H.K. Pathak, S.M. Kang, J.S. Jung, “Common fixed points of compatible maps of type on fuzzy metric spaces”, Fuzzy Sets and Systems, vol.93, pp.99-111, 1998.
[21] Z. K. Deng, “Fuzzy pseudo- metric spaces”, J. Math. Anal. Appl., vol.86, pp.74-95, 1982. .
Alok Asati , A.D.Singh , Madhuri Asati, "Fixed Point Theorem in Fuzzy Metric Space with Implicit relation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 9, no. 2, pp. 107-114, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V9P511