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On the Stability of Quartic Functional Equations via Fixed Point and Direct Method

by Renu Chugh, Ashish, Manoj Kumar
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 40 - Number 13
Year of Publication: 2012
Authors: Renu Chugh, Ashish, Manoj Kumar
10.5120/5041-7365

Renu Chugh, Ashish, Manoj Kumar . On the Stability of Quartic Functional Equations via Fixed Point and Direct Method. International Journal of Computer Applications. 40, 13 ( February 2012), 23-28. DOI=10.5120/5041-7365

@article{ 10.5120/5041-7365,
author = { Renu Chugh, Ashish, Manoj Kumar },
title = { On the Stability of Quartic Functional Equations via Fixed Point and Direct Method },
journal = { International Journal of Computer Applications },
issue_date = { February 2012 },
volume = { 40 },
number = { 13 },
month = { February },
year = { 2012 },
issn = { 0975-8887 },
pages = { 23-28 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume40/number13/5041-7365/ },
doi = { 10.5120/5041-7365 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:27:59.571642+05:30
%A Renu Chugh
%A Ashish
%A Manoj Kumar
%T On the Stability of Quartic Functional Equations via Fixed Point and Direct Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 40
%N 13
%P 23-28
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The purpose of this paper is to establish the Hyers-Ulam-Rassias stability of quartic functional equation f(3x+y)+f(x+3y)=64f(x)+64f(y)+24f(x+y)-6f(x-y) in the setting of random normed space and intuitionistic random normed space. The stability of the equation is proved by using the fixed point method and direct method.

References
  1. A. N. Sherstnev : On the notion of a random normed space. Dpkl. Akad. Nauk SSSR 149 (1963), pp. 280-283 (in Russian).
  2. B. Schweizer and A. Sklar, Probabilistic Metric Spaces. Elsevier, North Holand (1983).
  3. C. Jung, On generalized complete metric spaces. Bull Am Math Soc. 75 (1969), pp. 113–116.
  4. D. H. Hyers, On the Stability of the Linear Functional Equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), pp. 222–224.
  5. D. Mihe? and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces. J Math Anal. Appl. 343(2008), pp. 567–572.
  6. D. Mihe?, The stability of the additive Cauchy functional equation in non-Archimedean fuzzy normed spaces. Fuzzy Set Syst. 161 (2010), pp. 2206–2212.
  7. G. Deschrijver, and EE. Kerre, On the relationship between some extensions of fuzzy set theory. Fuzzy Set Syst. 23 (2003), pp. 227–235.
  8. O. Hadži? and E. Pap, Fixed Point Theory in PM-Spaces. Kluwer Academic, Dordrecht (2001)
  9. K. Atanassov, Intuitionistic fuzzy sets. Fuzzy Set Syst. 20 (1986), pp. 87–96.
  10. M. Petapirak and P. Nakmahachalasiant, A quartic functional equation and it Generalized Hyers-Ulam-Rassias stability, Thai J. of Mat., Sp. Iss.(2008) pp.77-84.
  11. P. Gavruta : A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings, J. Math. Anal. Appl. 184 (1994), pp.431–436.
  12. R. Saadati, J. Park, On the intuitionistic fuzzy topological spaces, Chaos Soliton Fract. 27(2006), pp. 331–344.
  13. S. Chang, J. Rassias and R. Saadati, The stability of the cubic functional equation in intuitionistic random normed spaces, Appl Math Mech. 31 (2010), pp. 21–26.
  14. S. Chang, Y. Cho and Y. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces. Nova Science Publishers Inc., NewYork (2001)
  15. S. Kutukcu, A. Tuna and A. Yakut, Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations. Appl Math Mech. 28 (2007) pp.799–809.
  16. S.M. Ulam : Problems on Modern Mathematics, John Wiley and Sons, New York, NY, USA, 1964.
  17. Th. M. Rassias, On the stability of the Linear mapping in Banach spaces, Procc. Of the American Mathematical Society, vol. 72(1978), no. 2, pp.297-300.
Index Terms

Computer Science
Information Sciences

Keywords

Fixed point method Quartic functional equation Random normed space intuitionistic random normed space

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