ON THE HYERS-ULAM-RASSIAS STABILITY OF JENSENS EQUATION

Title & Authors
ON THE HYERS-ULAM-RASSIAS STABILITY OF JENSENS EQUATION
Zhang, Dongyan; Wang, Jian;

Abstract
J. Wang [21] proposed a problem: whether the Hyers-Ulam-Rassias stability of Jensens equation for the case p, q, r, s $\small{\in}$ ($\small{\beta}$, $\small{\frac{1}{\beta}}$) \ {1} holds or not under the assumption that G and E are $\small{\beta}$-homogeneous Fspace (0 < $\small{\beta\;\leq}$ 1). The main purpose of this paper is to give an answer to Wangs problem. Furthermore, we proved that the stability property of Jensens equation is not true as long as p or q is equal to $\small{\beta}$, $\small{\frac{1}{\beta}}$, or $\small{\frac{\beta_2}{\beta_1}}$ (0 < $\small{\beta_1,\beta_2\leq}$ 1).
Keywords
Hyers-Ulam-Rassias stability;Jensens functional equation;
Language
English
Cited by
1.
Generalized stabilities of two functional equations, Aequationes mathematicae, 2013, 86, 3, 269
2.
Nearly Quartic Mappings in β-Homogeneous F-Spaces, Results in Mathematics, 2013, 63, 1-2, 529
3.
Mean square Hyers-Ulam stability of stochastic differential equations driven by Brownian motion, Advances in Difference Equations, 2016, 2016, 1
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