Stability Of a Quadratic Functional Equation in Intuitionistic Fuzzy Banach Spaces

Hyers-Ulam-Rassias stability theorem has been applied to several functional equations for studying stability in case of approximation of a given functional equation in Banach spaces, fuzzy Banach spaces etc. In this paper, we wish to study generalized Hyers-Ulam-Rassias stability regarding the approximationof the following quadratic functional equationf(2x + y) − f(x + 2y) = 3f(x) − 3f(y) (1)in intuitionistic fuzzy Banach spaces.

___

  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
  • C. Borelli, G. L. Forti, On a general Hyers Ulam stability, Internat. J. Math. Math.Sci., 18 (1995), 229 − 236.
  • P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27. 76 − 86 (1984).
  • S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62 (1992) , 59 − 64.
  • G. Deschrijiver, E. E. Kerre, on the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems 23 (2003), 227 − 235.
  • D. H. Hyers, On the stability of the linear functional equation, Proc. Nat.Acad.Sci.U.S.A. 27 (1941), 222 − 224.
  • Kil-Woung Jun, Hark-Mann Kim and Don o Lee, on the stability of a quadratic functional equation, J.Chungcheeng Math. Soc., volume 15, no.-2(Dec.2002), 73 −84 .
  • N. C. Kayal, P. Mondal, T. K. Samanta, The Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation in Fuzzy Banach Spaces, Journal of New Results in Science, 5 (2014) 83 − 95.
  • J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004), 1039 − 1046.
  • Th.M.Rassias, on the stability of the functional equations in Banach spaces, J.Math. Anal.Appl. 251(2000), 264 − 284.
  • R. Saadati, J. H. Park, On Intuitionistic fuzzy topological spaces , Chaos , Solitons and Fractals 27 (2006) ,331 − 344.
  • R. Saadati, J. H. Park, On Intuitionistic fuzzy Euclidean normed spaces, Commun. Math. Anal., 1 (2006) , 85 − 90.
  • T. K. Samanta, P. Mondal, N. C. Kayal, The generalized Hyers-Ulam-Rassias stability of a quadratic functional equation in fuzzy Banach spaces, Annals of Fuzzy Mathematics and Informatics Volume 6, No. 2, (2013), pp. 59 − 68.
  • S. Shakeri, Intutionistic fuzzy stability of Jenson Type Mapping, J.Non linear Sc. Appl.2 (2009),no.-2,105 − 112.
  • F. Skof, Proprieta locali e approssimazione di opratori, Rend. Sem. Mat. Fis. Milano, 53 (1983), 113 − 129.
  • S. M. Ulam, Problems in Modern Mathematics, Chapter vi, Science Editions, Wiley, New York, 1964.
  • L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965) 338 − 353.
Journal of New Results in Science-Cover
  • ISSN: 1304-7981
  • Yayın Aralığı: Yılda 3 Sayı
  • Başlangıç: 2012
  • Yayıncı: Tokat Gaziosmanpaşa Üniversitesi