Common fixed points for weak compatible maps in fuzzy metric spaces
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Abstract
In this note we shall prove common fixed point theorems for four mappings under weak compatible condition in the setting of fuzzy metric space, fuzzy 2-metric space, and fuzzy 3-metric spaces. Our results generalize the results of Singh, Jain and Jain.
References
[1] Y.J.Cho: Fixed point in fuzzy metric spaces, journal of fuzzy mathematics 5, 949 - 962(1997).
[2] B.C.Dhage: On common fixed point of coincidentally commuting mappings in D-metric spaces, Indian journal of pure and Applied Mathematics 30,395-406 (1999).
[3] S.Gahler:- 2-metricsche aume ihre topologische structure, Math.Nachr.26 (63-64), 115-148.
[4] A.George and P.Veeramani:- On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64, 395-399 (1994).
[5] M.Grabiec:- Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 7, 385-389 (1988).
View more references (19)
[6] V.Gregori, A.Spena:-On fixed point theorems in fuzzy metric spaces, Fuzzy sets and systems, 125 (2002) 245-252.
[7] G.Jungck:-Compatible mappings and common fixed point, International Journal of Mathematics and Mathematical Sciences 9, 771-779, (1986)
[8] G.Jungck and B.E.Rhoades:- Fixed point for set valued functions without continuity, Indian Journal of pure and Applied Mathematics 29,227-238 (1998).
[9] I.Kramosil and J.Michalek:-Fuzzy metric and statistical metric spaces, Kybernetica 11, 326-334 (1975).
[10] S.N.Mishra and S.L.Singh:- Common fixed point of maps in fuzzy metric spaces, International Journal of mathematics and Mathematical Sciences 17,253-258(1994).
[11] S.Sessa:- On a weak commutative condition in fixed point consideration, Publ.Inst. Math (Beograd) 32,146-153 (1982).
[12] S.Sharma; Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125(2001), 1-8.
[13] S.Sharma; Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 127(2002), 345-352.
[14] S.Sharma and B.Deshpande; Discontinuity and Weak compatibility in fixed point consideration on Non-complete fuzzy metric space, The Journal of Fuzzy Mathematics Vol.11, No.3 (2003), 671-686.
[15] B.Singh and Shishir Jain: - Semi compatibility and fixed point theorems in Menger space, Journal of Chingcheong Mathematical Society 17, 1-17 (2004).
[16] B.Singh and Shishir Jain: - A fixed point theorem in menger space through weak compatibility, Journal of Mathematical Analysis and Application 301, 439-448 (2005).
[17] B.Singh and Shishir Jain:- Semi- compatibility, Compatibility and fixed point theorems in fuzzy metric space, Journal of the Chungcheong Mathematical Society 18, 1-22 (2005).
[18] B.Singh, S. Jain and S.Jain; Generalized theorems on fuzzy metric spaces, Southeast Asian Bulletin of Mathematics (2007) 31, 963-978.
[19] G.Song, Comments on “A common fixed point theorem in a fuzzy metric space” Fuzzy sets and systems, 135 (2003) 409-413
[20] Sushil Sharma: - On fuzzy metric spaces, Southeast Asian Bulletin of Mathematics 26, 133-145 (2002).
[21] R.Vasuki:- Common fixed point theorem in a fuzzy metric space, Fuzzy Sets and Systems 97,395-397 (1998).
[22] R.Vasuki:- Common fixed points for R-weakly commuting maps in fuzzy metric space, Indian Journal of Pure and Applied Mathematics, 419-423 (1999).
[23] P.Vijayaraju, M.Marudai, Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems, 135 (2003) 401-408.
[24] L.A.Zadeh:- Fuzzy sets, Inform and control 89, 338-353 (1965).