×

zbMATH — the first resource for mathematics

Semicompatibility and fixed point theorems for reciprocally continuous maps in a fuzzy metric space. (English) Zbl 1213.54010
From the summary: The aim of this paper is to prove a common fixed point theorem for six mappings on fuzzy metric space using notion of semicompatibility and reciprocal continuity of maps satisfying an implicit relation.

MSC:
54A40 Fuzzy topology
54H25 Fixed-point and coincidence theorems (topological aspects)
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338-353, 1965. · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[2] O. Kramosil and J. Michalek, “Fuzzy metric and statistical metric spaces,” Kybernetika, vol. 11, pp. 326-334, 1975. · Zbl 0319.54002
[3] A. George and P. Veeramani, “On some results in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 64, no. 3, pp. 395-399, 1994. · Zbl 0843.54014 · doi:10.1016/0165-0114(94)90162-7
[4] V. Gregori and A. Sapena, “On fixed-point theorems in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 125, no. 2, pp. 245-252, 2002. · Zbl 0995.54046 · doi:10.1016/S0165-0114(00)00088-9
[5] D. Mihe\ct, “A Banach contraction theorem in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 144, no. 3, pp. 431-439, 2004. · Zbl 1052.54010 · doi:10.1016/S0165-0114(03)00305-1
[6] B. Schweizer, H. Sherwood, and R. M. Tardiff, “Contractions on probabilistic metric spaces: examples and counterexamples,” Stochastica, vol. 12, no. 1, pp. 5-17, 1988. · Zbl 0689.60019 · eudml:39008
[7] M. Grabiec, “Fixed points in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 27, no. 3, pp. 385-389, 1988. · Zbl 0664.54032 · doi:10.1016/0165-0114(88)90064-4
[8] R. Vasuki, “Common fixed points for R-weakly commuting maps in fuzzy metric spaces,” Indian Journal of Pure and Applied Mathematics, vol. 30, no. 4, pp. 419-423, 1999. · Zbl 0924.54010
[9] R. P. Pant, “Common fixed points of four mappings,” Bulletin of the Calcutta Mathematical Society, vol. 90, no. 4, pp. 281-286, 1998. · Zbl 0936.54043
[10] R. P. Pant and K. Jha, “A remark on common fixed points of four mappings in a fuzzy metric space,” Journal of Fuzzy Mathematics, vol. 12, no. 2, pp. 433-437, 2004. · Zbl 1054.54517
[11] P. Balasubramaniam, S. Muralisankar, and R. P. Pant, “Common fixed points of four mappings in a fuzzy metric space,” Journal of Fuzzy Mathematics, vol. 10, no. 2, pp. 379-384, 2002. · Zbl 1022.54004
[12] V. Popa, “Some fixed point theorems for weakly compatible mappings,” Radovi Matemati\vcki, vol. 10, no. 2, pp. 245-252, 2001. · Zbl 1064.54506
[13] B. Singh and S. Jain, “Semi-compatibility, compatibility and fixed point theorem in fuzzy metric space,” Journal of the Chuncheong Mathematical Society, pp. 1-22, 2005. · Zbl 1162.54328
[14] B. Singh and M. S. Chauhan, “Common fixed points of compatible maps in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 115, no. 3, pp. 471-475, 2000. · Zbl 0985.54009 · doi:10.1016/S0165-0114(98)00099-2
[15] B. Singh and S. Jain, “Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation,” International Journal of Mathematics and Mathematical Sciences, no. 16, pp. 2617-2629, 2005. · Zbl 1087.54506 · doi:10.1155/IJMMS.2005.2617 · eudml:52354
[16] M. Imdad, S. Kumar, and M. S. Khan, “Remarks on some fixed point theorems satisfying implicit relations,” Radovi Matemati\vcki, vol. 11, no. 1, pp. 135-143, 2002. · Zbl 1033.54025
[17] V. Popa, “Fixed points for non-surjective expansion mappings satisfying an implicit relation,” Buletinul \cStiin\ctific al Universit\ua\ctii Baia Mare. Seria B, vol. 18, no. 1, pp. 105-108, 2002. · Zbl 1031.47034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.