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

Authors

  • Wudthichai Onsod KMUTT Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok
  • Poom Kumam MUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok

DOI:

https://doi.org/10.26713/cma.v7i3.416

Keywords:

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

Abstract

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.

Downloads

Download data is not yet available.

References

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.

Downloads

Published

14-11-2016
CITATION

How to Cite

Onsod, W., & Kumam, P. (2016). Common Fixed Point Results for \((\phi,\psi)\)-Weak Contraction Mappings via \(f\)-\(\alpha\)-Admissible Mappings in Intuitionistic Fuzzy Metric Spaces. Communications in Mathematics and Applications, 7(3), 167–178. https://doi.org/10.26713/cma.v7i3.416

Issue

Section

Research Article