대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제46권4호
  • /
  • Pages.645-656
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  • 2009
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 발행 : 2009.07.31
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초록

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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참고문헌

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피인용 문헌

  1. Generalized stabilities of two functional equations vol.86, pp.3, 2013, https://doi.org/10.1007/s00010-012-0180-8
  2. Nearly Quartic Mappings in β-Homogeneous F-Spaces vol.63, pp.1-2, 2013, https://doi.org/10.1007/s00025-011-0215-9
  3. Mean square Hyers-Ulam stability of stochastic differential equations driven by Brownian motion vol.2016, pp.1, 2016, https://doi.org/10.1186/s13662-016-1002-4