In this paper, we prove a stability result for the additive Cauchy functional equation in random normed spaces, related to the main theorem from the paper [D. MiheΕ£, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008) 567-572]
The stability of the quartic functional equation in various spaces
β Scribed by Reza Saadati; Yeol J. Cho; Javad Vahidi
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 325 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0898-1221
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π SIMILAR VOLUMES
The paper is devoted to some results on the problem of S. M. Ulam for the stability of functional equations in Banach spaces. The problem was posed by Ulam 60 years ago.
Making use of the fundamental solution of the heat equation we prove the stability theorems of quadratic functional equation and d'Alembert equation in the spaces of Schwartz distributions and Sato hyperfunctions.
Making use of the fundamental solution of the heat equation we reformulate and prove the stability theorem of a special case of the Euler-Lagrange-Rassias functional equation in the spaces of tempered distributions and Fourier hyperfunctions.
In this paper, we will introduce a new multiplicative functional Eq. 1 and prove Ε½ . that the given equation is equivalent to the well known ''original'' one, f xy s Ε½ . Ε½ . Ε½ . f x f y . Moreover, we will investigate the stability problem of Eq. 1 in the sense of R. Ger.