Abstract
In this paper, we investigate the Hyers–Ulam stability of the following quartic equation
\(({n \in \mathbb{N}, n \geq 3})\) in β-homogeneous F-spaces.
Similar content being viewed by others
References
Aoki T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)
Czerwik S.: On the stability of the quadratic mapping in normed spaces. Abh. Math. Sem. Univ. Hamburg 62, 59–64 (1992)
Eshaghi Gordji M., Khodaei H.: Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi–Banach spaces. Nonlinear Anal. TMA 71, 5629–5643 (2009)
Gǎvruta P.: A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)
Hyers D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. 27, 222–224 (1941)
Jun K.W., Kim H.M.: The generalized Hyers–Ulam–Rassias stability of a cubic functional equation. J. Math. Anal. Appl. 274, 867–878 (2002)
Jung S.-M.: Hyers–Ulam–Rassias stability of Jensen’s equation and its application. Proc. Am. Math. Soc. 126, 3137–3143 (1998)
Kominek Z.: On a local stability of the Jensen functional equation. Demonstr. Math. 22, 499–507 (1989)
Lee S.H., Im S.M., Hwang I.S.: Quartic functional equations. J. Math. Anal. Appl. 307, 387–394 (2005)
Rassias Th.M.: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)
Rolewicz S.: Metric Linear Spaces. PWN–Polish Scientific Publishers, Warsaw (1972)
Ulam S.M.: Problems in Modern Mathematics, Chapter VI, Science ed. Wiley, New York (1940)
Wang J.: Some further generalizations of the Hyers–Ulam–Rassias stability of functional equations. J. Math. Anal. Appl. 263, 406–423 (2001)
Wang J.: On the generalizations of the stability of Pexider equations and Jensen equations. Nonlinear Funct. Anal. Appl. 7, 229–239 (2002)
Wang J.: The additive approximation on a four-variate Jensen-type operator equation. Int. J. Math. Math. Sci 50, 3171–3187 (2003)
Zhang D., Wang J.: On the Hyers–Ulam–Rassias stability of Jensen’s equation. Bull. Korean Math. Soc. 46, 645–656 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, I.S., Eshaghi Gordji, M., Khodaei, H. et al. Nearly Quartic Mappings in β-Homogeneous F-Spaces. Results. Math. 63, 529–541 (2013). https://doi.org/10.1007/s00025-011-0215-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-011-0215-9