• 호남수학학술지
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• 제30권3호
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• 대한수학회논문집
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• 제31권1호
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• pp.101-113
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• 2016

In this article, we considered the stability of the following (${\alpha}$, ${\beta}$, ${\gamma}$)-derivation $${\alpha}D[x,y]={\beta}[D(x),y]+{\gamma}[x,D(y)]$$ and homomorphisms associated to the quadratic type functional equation $$f(kx+y)+f(kx+{\sigma}(y))=2kg(x)+2g(y),\;x,y{\in}A$$, where ${\sigma}$ is an involution of the Lie $C^*$-algebra A and k is a fixed positive integer. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.429-445
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• 2004

In this paper we investigate the generalized Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(x,y)){\;}={\;}\phi(x,y)f(x,y)$, where x, y lie in the set S. As a consequence we obtain stability in the sense of Hyers, Ulam, Rassias, Gavruta, for some well-known equations such as the gamma, beta and G-function type equations.

• 대한수학회논문집
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• 제20권2호
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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.

• 대한수학회논문집
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• 제23권3호
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• pp.357-369
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• 2008

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.193-198
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• 2012

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.1017-1027
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• 2000

On the positive real number, we obtain the Hyers-Ulam stability and a stability in the sense of R. Ger for the generalized beta function g(x+p,y+q) = ${\varphi}(x,y)g(x,y)$ in the following settings: $$\mid$g(x+p,y+q)-{\varphi}(x,y)g(x,y)$\mid${\leq}{\delta}$ and $$\mid$\frac{g(x+p,y+q)}{\varphi(x,y)g(x,y)}-1$\mid${\leq}{\psi}(x,y). As a consequence we obtain stability theorems for the gamma functional equation and the beta functional equation.

• KSBB Journal
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• 제20권2호
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• pp.106-111
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• 2005

물고기 기름을 구성하고 있는 15종류 지방산에 대한 mol수와 가수분해 시간 사이의 함수관계를 대수함수식, $S_i=-{\alpha_i}1n(t)+{\beta_i}$로 나타내었다. 동일 가수분해 시간에서 각 지방산에 대한 대수함수식의 $S_i$ 값과 실측치 사이의 오차가 15 종류 지방산 모두에 대하여 $5\%$ 이내에 분포되었다. 각 지방산의 mol수 $S_i$와 가수분해 시간 사이의 대수함수식으로부터 각 지방산에 대한 가수분해 반응속도를 지방산 mol 수의 지수함수 관계식, $v_i={\gamma_i}exp(\frac{S_i}{\alpha_i})$로 유도하였다. 또한 유도된 $S_i$와 t 사이의 함수관계식으로부터 물고기 기름을 구성하는 15 종류 지방산 각각에 대한 가수분해율을 분석하였다. 가수분해 시간 48시간에서 가수분해율이 $70\%$ 이상인 지방산은 C14:0, C16:0, C18:0, C16:1, C18:1(n-7) 및 Cl8:1(n-9)이였으며, 가수분해율이 $40\%$ 내지 $60\%$ 사이에 분포되어 있는 지방산은 C20:1, C22:1, C18:3, C18:4, C20:4 및 C20:5이였으며, 가수분해율이 $30\%$ 내외인 지방산은 C2l:5와 C22:5이였으며, $20\%$ 이하인 지방산은 C22:6이였다.