Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE HYERS-ULAM-RASSIAS STABILITY OF JENSEN'S EQUATION

  • Zhang, Dongyan (SCIENCE INSTITUTE INFORMATION ENGINEERING UNIVERSITY) ;
  • Wang, Jian (DEPARTMENT OF MATHEMATICS FUJIAN NORMAL UNIVERSITY)
  • Published : 2009.07.31
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Abstract

J. Wang [21] proposed a problem: whether the Hyers-Ulam-Rassias stability of Jensen's equation for the case p, q, r, s $\in$ ($\beta$, $\frac{1}{\beta}$) \ {1} holds or not under the assumption that G and E are $\beta$-homogeneous Fspace (0 < $\beta\;\leq$ 1). The main purpose of this paper is to give an answer to Wang's problem. Furthermore, we proved that the stability property of Jensen's equation is not true as long as p or q is equal to $\beta$, $\frac{1}{\beta}$, or $\frac{\beta_2}{\beta_1}$ (0 < $\beta_1,\beta_2\leq$ 1).

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