Skip to content
IJAMR International Journal of Applied Mathematical Research E-ISSN 2227-4324

Common fixed points for weak compatible maps in fuzzy metric spaces

Authors and Affiliations

  • praveen kumar sharma IES , IPS Academy Indore-452012 M.P. INDIA
  • sanjay choudhary Govt. Narmada Mahavidhalaya Hoshangabad (M.P.), India
  • kamal wadhwa Govt. Narmada Mahavidhalaya Hoshangabad (M.P.), India

About this article

Download PDF

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.

Author Biographies

  • praveen kumar sharma, IES , IPS Academy Indore-452012 M.P. INDIA

    Lecturer (mathematics)

    Department of mathematics

    IES , IPS Academy
    Indore-452012
    M.P.
    INDIA
  • sanjay choudhary, Govt. Narmada Mahavidhalaya Hoshangabad (M.P.), India
    Professor and Head department of Mathematics, Govt. Narmada Mahavidhalaya Hoshangabad (M.P.), India
  • kamal wadhwa, Govt. Narmada Mahavidhalaya Hoshangabad (M.P.), India

    Asst. Professor of Mathematics, Govt. Narmada Mahavidhalaya Hoshangabad (M.P.), India

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).


How to Cite

sharma, praveen kumar, choudhary, sanjay, & wadhwa, kamal. (2012). Common fixed points for weak compatible maps in fuzzy metric spaces. International Journal of Applied Mathematical Research, 1(2), 159-177. https://doi.org/10.14419/ijamr.v1i2.61