• 대한수학회논문집
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• 제16권4호
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• pp.607-619
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• 2001

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

• 대한수학회논문집
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• 제20권1호
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• pp.93-106
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• 2005

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.291-305
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• 2018

In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

• 대한수학회보
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• 제44권4호
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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.

• 충청수학회지
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• 제31권2호
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• pp.199-230
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• 2018

In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.

• 충청수학회지
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• 제22권3호
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• pp.383-398
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• 2009

In this paper, we study the generalized Hyers-Ulam stability of a bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,w)+f(y,\;z)+f(y,w)$$. Moreover, we establish stability results on the punctured domain.

• 충청수학회지
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• 제21권2호
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• pp.165-174
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• 2008

In this paper, we obtain the general solution, the generalized Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a cubic functional equation $4f(x+my)+4f(x-my)+m^2f(2x)=8f(x)+4m^2f(x+y)+4m^2f(x-y)$ for a positive integer $m{\geq}2$.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.671-684
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• 2023

In this paper, we prove the generalized Hyers-Ulam stability of a general quintic functional equation, $\sum\limits_{k=0}^{6}(-1)^k{_6}C_kf(x+(3-k)y)=0$, by using the fixed point method.

• 충청수학회지
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• 제20권4호
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• pp.515-523
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• 2007

In this paper, we investigate the Hyers-Ulam-Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.

• 대한수학회보
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• 제46권1호
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• pp.87-97
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• 2009

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.