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. We proposed to reanalysis the theorems of Imdad et al. (2002), Popa (2001), Popa (2002) and Singh and Jain (2005).
References
L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. 0139.24606 MR219427 L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. 0139.24606 MR219427
A. George and P. Veeramani, “On some results in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 64, no. 3, pp. 395–399, 1994. 0843.54014 MR1289545 10.1016/0165-0114(94)90162-7 A. George and P. Veeramani, “On some results in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 64, no. 3, pp. 395–399, 1994. 0843.54014 MR1289545 10.1016/0165-0114(94)90162-7
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. 0995.54046 MR1880341 10.1016/S0165-0114(00)00088-9 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. 0995.54046 MR1880341 10.1016/S0165-0114(00)00088-9
D. Miheţ, “A Banach contraction theorem in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 144, no. 3, pp. 431–439, 2004. 1052.54010 MR2061405 10.1016/S0165-0114(03)00305-1 D. Miheţ, “A Banach contraction theorem in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 144, no. 3, pp. 431–439, 2004. 1052.54010 MR2061405 10.1016/S0165-0114(03)00305-1
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. 0689.60019 MR1004655 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. 0689.60019 MR1004655
M. Grabiec, “Fixed points in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 27, no. 3, pp. 385–389, 1988. 0664.54032 MR956385 10.1016/0165-0114(88)90064-4 M. Grabiec, “Fixed points in fuzzy metric spaces,” Fuzzy Sets and Systems, vol. 27, no. 3, pp. 385–389, 1988. 0664.54032 MR956385 10.1016/0165-0114(88)90064-4
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. MR1695690 0924.54010 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. MR1695690 0924.54010
R. P. Pant, “Common fixed points of four mappings,” Bulletin of the Calcutta Mathematical Society, vol. 90, no. 4, pp. 281–286, 1998. 0936.54043 MR1697238 R. P. Pant, “Common fixed points of four mappings,” Bulletin of the Calcutta Mathematical Society, vol. 90, no. 4, pp. 281–286, 1998. 0936.54043 MR1697238
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. 1054.54517 MR2065008 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. 1054.54517 MR2065008
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. 1022.54004 MR1908630 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. 1022.54004 MR1908630
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. 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.
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. 0985.54009 MR1781548 10.1016/S0165-0114(98)00099-2 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. 0985.54009 MR1781548 10.1016/S0165-0114(98)00099-2
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. 1087.54506 MR2184754 10.1155/IJMMS.2005.2617 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. 1087.54506 MR2184754 10.1155/IJMMS.2005.2617
M. Imdad, S. Kumar, and M. S. Khan, “Remarks on some fixed point theorems satisfying implicit relations,” Radovi Matematički, vol. 11, no. 1, pp. 135–143, 2002. 1033.54025 MR1971330 M. Imdad, S. Kumar, and M. S. Khan, “Remarks on some fixed point theorems satisfying implicit relations,” Radovi Matematički, vol. 11, no. 1, pp. 135–143, 2002. 1033.54025 MR1971330
V. Popa, “Fixed points for non-surjective expansion mappings satisfying an implicit relation,” Buletinul Ştiinţific al Universităţii Baia Mare. Seria B, vol. 18, no. 1, pp. 105–108, 2002. 1031.47034 MR2014290 V. Popa, “Fixed points for non-surjective expansion mappings satisfying an implicit relation,” Buletinul Ştiinţific al Universităţii Baia Mare. Seria B, vol. 18, no. 1, pp. 105–108, 2002. 1031.47034 MR2014290
