Stability Of a Quadratic Functional Equation in Intuitionistic Fuzzy Banach Spaces

Year 2016, Volume: 5 Issue: 10, 52 - 59, 05.05.2016

Pratap Mondal Nabin Chandra Kayal T K Samanta

Abstract

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 approximation
of the following quadratic functional equation
f(2x + y) − f(x + 2y) = 3f(x) − 3f(y) (1)
in intuitionistic fuzzy Banach spaces.

Keywords

Intuitionistic fuzzy norm, Hyers-Ulam stability, quadratic functional equation, Intuitionistic fuzzy Banach spaces

References

• 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.