Tbilisi Mathematical Journal

Intuitionistic fuzzy stability of a quadratic functional equation

Nabin Chandra Kayal, Pratap Mondal, and T. K. Samanta

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The aim of this paper is to determine Hyers-Ulam-Rassias Stability results concerning the quadratic functional equation, $f(2x \,+\,y)\,+ \, f(2x\,-\,y)\, =\,2f(x\,+\,y)\,+\,2f(x\,-\,y)\,+\,4f(x)\,-\,2f(y)$ in intuitionistic fuzzy Banach spaces.

Article information

Tbilisi Math. J., Volume 8, Issue 2 (2015), 139-147.

Received: 25 November 2014
Accepted: 17 June 2015
First available in Project Euclid: 12 June 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E72: Fuzzy set theory
Secondary: 97I70: Functional equations 39B82: Stability, separation, extension, and related topics [See also 46A22]

t-norm t-conorm Intuitionistic fuzzy normed space Quadratic functional equation Hyers-Ulam-Rassias stability


Kayal, Nabin Chandra; Mondal, Pratap; Samanta, T. K. Intuitionistic fuzzy stability of a quadratic functional equation. Tbilisi Math. J. 8 (2015), no. 2, 139--147. doi:10.1515/tmj-2015-0017. https://projecteuclid.org/euclid.tbilisi/1528769013

Export citation


  • D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 $(1941)$, 222$-$224.
  • F. Skof, Proprieta locali e approssimazione di opratori, Rend. Sem. Mat. Fis. Milano, 53 $(1983)$, 113$-$129.
  • G. Deschrijver, C. Cornelis and E. E. Kerre, On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Transaction on Fuzzy Systems, 12 $( 2004 )$, 45$-$61.
  • G. Deschrijver, E. E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems, 23 $( 2003 )$, 227$-$235.
  • J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 $( 2004 )$, 1039$-$1046.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 $( 1986 )$, 87$-$96.
  • N. Chandra Kayal, P. Mondal and T. K. Samanta The Generalized Hyers - Ulam - Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces, Journal of New Results in Science, 1 (5) $(2014)$, 83$-$95.
  • N. Chandra Kayal, P. Mondal and T. K. Samanta, The Fuzzy Stability of a Pexiderized Functional Equation, Mathematica Moravica, 18 (2) $(2014)$, 1$-$14.
  • P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. appl., 184 $(1994)$, 431$-$436.
  • P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27 $(1984)$, 76$-$86.
  • R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons and Fractals, 27 $( 2006 )$, 331$-$344.
  • S. Czerwik, On the stability of the quadratic mappings in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62 $(1992)$, 59$-$64.
  • S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science Editions, Wiley, New York, 1960.
  • S. Shakeri, Intutionistic fuzzy stability of Jenson type mapping, J. Non linear Sc. Appl., 2 $(2009)$, no.-2, 105$-$112.
  • T. Aoki, On the Stability of Linear Transformation in Banach Spaces, J. Math. Soc. Japan, 2 $(1950)$, 64$-$66.
  • Th. M. Rassias, On the stability of the linear mapping in Banach space, Proc. Amer. Mathematical Society, 72(2) $(1978)$, 297$-$300.
  • T. K. Samanta, N. Chandra Kayal and P. Mondal, The Stability of a General Quadratic Functional Equation in Fuzzy Banach Space, Journal of Hyperstructures, 1 (2) $(2012)$, 71$-$87.