Common Fixed Point Results for \((\phi,\psi)\)-Weak Contraction Mappings via \(f\)-\(\alpha\)-Admissible Mappings in Intuitionistic Fuzzy Metric Spaces

Wudthichai Onsod, Poom Kumam


In this paper, by using the concept of \(f\)-\(\alpha\)-admissible mappings, we prove common fixed point in intuitionistic fuzzy metric spaces. We also introduce the notion of \(f\)-\(\alpha\)-\(\phi\)-\(\psi\)-weak contraction mappings in intuitionistic fuzzy metric spaces. The presented theorems extend, generalize and improve the corresponding results which given in the literature.


Common fixed point; Intuitionistic fuzzy metric space; \(\alpha\)-admissible; \((\phi,\psi)\)-weak contractions

Full Text:



M. Abbas, M. Imdad and D. Gopal, (psi)-weak contractions in fuzzy metric spaces, Iranian Journal of Fuzzy Systems 8 (2011), 141–148.

K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96.

S. Banach, Sur les operations dans les ensembles abstrits et leur application aux equations integrals, Fund. Math. 3 (1922), 133–181.

I. Beg, C. Vetro, D. Gopal and M. Imdad, ((phi,psi))-weak contractions in intuitionistic fuzzy metric spaces, Journal of Intelligent & Fuzzy Systems 26 (2014), 2497–2504.

V. Gregori, S. Romaguera and P. Veeramani, A note on intuitionistic fuzzy metric space, Chaos Solitons Fractals 28 (2006), 902–905.

A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395–399.

S. Heilpern, Fuzzy mappings and fixed point theorems, J. Math. Anal. Appl. 83 (1981), 56–569.

M. Imdad and Jaavid Ali, A general fixed point theorem in fuzzy metric spaces via an implicit function, Journal of Applied Mathematics & Informatics 26 (2008), 591–603.

Z. Jiao, On fixed point theorems in intuitionistic fuzzy metric spaces, Journal of Applied Mathematics 2012 (2012), Article ID 474983, 9 pages.

G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East Journal of Mathematical Sciences 4 (1996), 199–215.

G. Jungck, Compatible mapping and common fixed point, Internat. J. Math. Sci. 9 (1986), 771–779.

M.S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the point, Bulletin of the Australian Mathematical Society 30 (1984), 1–9.

R. Lowen, On Fuzzy Set Theory, Kluwer Academic Publishers, Dordrecht (1996).

J.H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 22 (2004), 1039–1046.

M. Rafi and M.S.M. Noorani, Fixed point theorems on intuitionistic fuzzy metric spaces, Iranian Journal of Fuzzy Systems 3 (2006), 23–29.

V.L. Rosa and P. Vetro, Common fixed points for (alpha)-(psi)-(phi)-contractions in generalized metric spaces, Nonlinear Analysis: Modelling and Comtrol 19 (2014), 43–54.

R. Saadati, S. Sedghi and N. Shobe, Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos Solitons Fractals 38 (2008), 36–47.

I. Schweizer and A. Sklar, Statistical metric spaces, Pacific Journal of Mathematics 10 (1960), 314–334.

C. Vetro, D. Gopal and M. Imdad, Common fixed points theorems for ((phi,psi))-weak contractions fuzzy metric spaces, Indian Journal of Mathematics 52 (2010), 573–590.

L.A. Zadeh, Fuzzy sets, Information & Control 8 (1965), 338–353.


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905