Research Article
On the Stability of Quadratic-Quartic (Q2Q4) Functional Equation over Non-Archimedean Normed Space
* Corresponding author
Abstract
In the present work the stability of Hyers-Ulam mixed type of quadratic-quartic Cauchy functional equation
g(2x+y)+g(2x−y)=4g(x+y)+4g(x−y)+2g(2x)−8g(x)−6g(y)
has been proved over Non-Archimedean normed space.
How to Cite
A. Ramachandran, S. Sangeetha, On the Stability of Quadratic-Quartic (Q2Q4) Functional Equation over Non-Archimedean Normed Space, Int. J. Anal. Appl. 22 (2024), 18. https://doi.org/10.28924/2291-8639-22-2024-18
BibTeX
@article{Ramachandran2024,
author = {Ramachandran, A. and Sangeetha, S.},
title = {On the Stability of Quadratic-Quartic (Q2Q4) Functional Equation over Non-Archimedean Normed Space},
journal = {Int. J. Anal. Appl.},
volume = {22},
year = {2024},
pages = {18},
doi = {10.28924/2291-8639-22-2024-18}
}References
- [1] T. Aoki, On the Stability of the Linear Transformation in Banach Spaces, J. Math. Soc. Japan. 2 (1950), 64–66. https://doi.org/10.2969/jmsj/00210064.
- [2] G. Bachman, Introduction to p-Adic Numbers and Valuation Theory, Academic Press, 1964.
- [3] D.G. Bourgin, Classes of Transformations and Bordering Transformations, Bull. Amer. Math. Soc. 57 (1951), 223–237.
- [4] A. Ebadian, A. Najati, M.E. Gordji, On Approximate Additive–Quartic and Quadratic–Cubic Functional Equations in Two Variables on Abelian Groups, Results. Math. 58 (2010), 39–53. https://doi.org/10.1007/s00025-010-0018-4.
- [5] M. Eshaghi Gordji, H. Khodaei, R. Khodabakhsh, General Quartic–cubic–quadratic Functional Equation in NonArchimedean Normed Spaces, U.P.B. Sci. Bull. Ser. A. 72 (2010), 69–84.
- [6] M. Eshaghi Gordji, M.B. Savadkouhi, Stability of Cubic and Quartic Functional Equations in Non-Archimedean Spaces, Acta Appl. Math. 110 (2009), 1321–1329. https://doi.org/10.1007/s10440-009-9512-7.
- [7] Z. Gajda, On Stability of Additive Mappings, Int. J. Math. Math. Sci. 14 (1991), 431–434.
- [8] M.E. Gordji, S. Abbaszadeh, C. Park, On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces, J. Inequal. Appl. 2009 (2009), 153084. https://doi.org/10.1155/2009/153084.
- [9] M.E. Gordji, M.B. Savadkouhi, C. Park, Quadratic-Quartic Functional Equations in RN-Spaces, J. Inequal. Appl. 2009 (2009), 868423. https://doi.org/10.1155/2009/868423.
- [10] M.E. Gordji, S.K. Gharetapeh, J.M. Rassias, S. Zolfaghari, Solution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation, Adv. Differ. Equ. 2009 (2009), 826130. https://doi.org/10.1155/2009/826130.
- [11] K. Hensel, Über eine neue Begründung der Theorie der Algebraischen Zahlen, Jahresber. Dtsch. Math.-Ver. 6 (1897), 83–88. https://eudml.org/doc/144593.
- [12] D.H. Hyers, G. Isac, Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Boston, 1998.
- [13] Y.S. Lee, S. Kim, C. Kim, Stability for the Mixed Type of Quartic and Quadratic Functional Equations, J. Funct. Spaces. 2014 (2014), 853743. https://doi.org/10.1155/2014/853743.
- [14] S.M. Mohammad, T. Rassias M., Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discr. Math. 1 (2007), 325–334. https://doi.org/10.2298/aadm0702325m.
- [15] A. Ramachandran, S. Sangeetha, On the Generalized Quadratic-Quartic Cauchy Functional Equation and its Stability over Non-Archimedean Normed Space, Math. Stat. 10 (2022), 1210–1217. https://doi.org/10.13189/ms.2022.100607.
- [16] Th.M. Rassias, On the Stability of the Linear Mapping in Banach Spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.
- [17] A.M. Robert, A Course in p-Adic Analysis, Springer, New York, 2000.
- [18] S.M. Ulam, Problems in Modern Mathematics, John Wiley & Sons, New York, 1940.
- [19] A.C.M. van Rooij, Non-Archimedean Functional Analysis, Monographs and Textbooks in Pure and Applied Mathematics, 51, Marcel Dekker, New York, 1978.