• Title/Summary/Keyword: generalized Hyers-Ulam stability

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ON HYERS-ULAM STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS

  • Huang, Jinghao;Jung, Soon-Mo;Li, Yongjin
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.685-697
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    • 2015
  • We investigate the stability of nonlinear differential equations of the form $y^{(n)}(x)=F(x,y(x),y^{\prime}(x),{\cdots},y^{(n-1)}(x))$ with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.

THE STABILITY OF THE GENERALIZED FORM FOR THE GAMMA FUNCTIONAL EQUATION

  • Kim, Gwang-Hui;Lee, Young-Whan
    • Communications of the Korean Mathematical Society
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    • v.15 no.1
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    • pp.45-50
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    • 2000
  • The modified Hyers-Ulam-Rassias Stability Of the generalized form g(x+p) : $\phi$(x)g(x) for the Gamma functional equation shall be proved. As a consequence we obtain the stability theorems for the gamma functional equation.

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HYERS{ULAM STABILITY OF FUNCTIONAL INEQUALITIES ASSOCIATED WITH CAUCHY MAPPINGS

  • Kim, Hark-Mahn;Oh, Jeong-Ha
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.4
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    • pp.503-514
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    • 2007
  • In this paper, we investigate the generalized Hyers-Ulam stability of the functional inequality $$||af(x)+bf(y)+cf(z)||{\leq}||f(ax+by+cz))||+{\phi}(x,y,z)$$ associated with Cauchy additive mappings. As a result, we obtain that if a mapping satisfies the functional inequality with perturbing term which satisfies certain conditions then there exists a Cauchy additive mapping near the mapping.

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THE GENERALIZED HYERS-ULAM STABILITY OF QUADRATIC FUNCTIONAL EQUATION WITH AN INVOLUTION IN NON-ARCHIMEDEAN SPACES

  • Kim, Chang Il;Shin, Chang Hyeob
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.2
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    • pp.261-269
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    • 2014
  • In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation $$(k+1)f(x+y)+f(x+{\sigma}(y))+kf({\sigma}(x)+y)-2(k+1)f(x)-2(k+1)f(y)=0$$ with an involution ${\sigma}$ for a fixed non-zero real number k with $k{\neq}-1$.

ON THE HYERS-ULAM STABILITY OF A GENERALIZED QUADRATIC AND ADDITIVE FUNCTIONAL EQUATION

  • JUN, KIL-WOUNG;KIM, HARK-MAHN
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.133-148
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    • 2005
  • In this paper, we obtain the general solution of a gen-eralized quadratic and additive type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a $\neq$ -1. 0, 1 in the class of functions between real vector spaces and investigate the generalized Hyers- Ulam stability problem for the equation.

GENERALIZED HYERS-ULAM STABILITY OF ADDITIVE FUNCTIONAL EQUATIONS

  • Kim, Hark-Mahn;Son, Eun-Yonug
    • The Pure and Applied Mathematics
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    • v.16 no.3
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    • pp.297-306
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    • 2009
  • In this paper, we obtain the general solution and the generalized HyersUlam stability theorem for an additive functional equation $af(x+y)+2f({\frac{x}{2}}+y)+2f(x+{\frac{y}{2})=(a+3)[f(x)+f(y)]$for any fixed integer a.

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