• Title, Summary, Keyword: Hyers-Ulam-Rassias stability

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HYERS-ULAM-RASSIAS STABILITY OF A SYSTEM OF FIRST ORDER LINEAR RECURRENCES

  • Xu, Mingyong
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.841-849
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    • 2007
  • In this paper we discuss the Hyers-Ulam-Rassias stability of a system of first order linear recurrences with variable coefficients in Banach spaces. The concept of the Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. As an application, the Hyers-Ulam-Rassias stability of a p-order linear recurrence with variable coefficients is proved.

HYERS-ULAM-RASSIAS STABILITY OF A CUBIC FUNCTIONAL EQUATION

  • Najati, Abbas
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.825-840
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    • 2007
  • In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

On a general hyers-ulam stability of gamma functional equation

  • Jung, Soon-Mo
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.437-446
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    • 1997
  • In this paper, the Hyers-Ulam stability and the general Hyers-Ulam stability (more precisely, modified Hyers-Ulam-Rassias stability) of the gamma functional equation (3) in the following setings $$ \left$\mid$ f(x + 1) - xf(x) \right$\mid$ \leq \delta and \left$\mid$ \frac{xf(x)}{f(x + 1)} - 1 \right$\mid$ \leq \frac{x^{1+\varepsilon}{\delta} $$ shall be proved.

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ON THE STABILITY OF FUNCTIONAL EQUATIONS IN n-VARIABLES AND ITS APPLICATIONS

  • KIM, GWANG-HUI
    • Communications of the Korean Mathematical Society
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    • v.20 no.2
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    • pp.321-338
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    • 2005
  • In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))\;=\;\phi(X)f(X)$, where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and Gavruta for many other equations such as the gamma, beta, Schroder, iterative, and G-function type's equations.

HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

  • Trif, Tiberiu
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.253-267
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    • 2003
  • In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.

APPROXIMATELY ADDITIVE MAPPINGS OVER p-ADIC FIELDS

  • Park, Choonkil;Boo, Deok-Hoon;Rassias, Themistocles M.
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.1
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    • pp.1-14
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    • 2008
  • In this paper, we prove the Hyers-Ulam-Rassias stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and of the Jensen functional equation $2f(\frac{x+y}{2})=f(x)+f(y)$ over the p-adic field ${\mathbb{Q}}_p$. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

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