• Honam Mathematical Journal
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• v.26 no.1
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• pp.45-59
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• 2004

In this paper we obtain the general solution the functional equation $a^2f(\frac{x-2y}{a})+f(x)+2f(y)=2a^2f(\frac{x-y}{a})+f(2y).$ The type of the solution of this equation is Q(x)+A(x)+C, where Q(x), A(x) and C are quadratic, additive and constant, respectively. Also we prove the stability of this equation in the spirit of Hyers, Ulam, Rassias and $G\check{a}vruta$.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.451-462
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• 2009

In this paper we prove the superstability of a generalized exponential functional equation $f(x+y)=a^{2xy-1}g(x)f(y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker. Also we investigate the stability of this functional equation in the following form : ${\frac{1}{1+{\delta}}}{\leq}{\frac{f(x+y)}{a^{2xy-1}g(x)f(y)}}{\leq}1+{\delta}$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.1-18
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• 2012

The aim of this paper is to investigate the superstability of the pexider type sine(hyperbolic sine) functional equation $f(\frac{x+y}{2})^{2}-f(\frac{x+{\sigma}y}{2})^{2}={\lambda}g(x)h(y),\;{\lambda}:\;constant$ which is bounded by the unknown functions ${\varphi}(x)$ or ${\varphi}(y)$. As a consequence, we have generalized the stability results for the sine functional equation by P. M. Cholewa, R. Badora, R. Ger, and G. H. Kim.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.61-74
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• 2007

Th. M. Rassias obtained the Hyers-Ulam stability of the general Euler-Lagrange functional equation. In this paper we prove the stability of generlized Euler-Lagrange functional equations in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruta.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.701-713
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• 2004

We obtain the Hyers-Ulam-Rassias stability of a betatype functional equation $f(\varphi(x),\phi(y))$ = $ \psi(x,y)f(x,y)+ \lambda(x,y)$ with a restricted domain and the stability in the sense of R. Ger of the equation $f(\varphi(x),\phi(y))$ = $ \psi(x,y)f(x,y)$ with a restricted domain in the following settings: $g(\varphi(x),\phi(y))-\psi(x,y)g(s,y)-\lambda(x,y)$\mid$\leq\varepsilon(x,y)$ and $\frac{g(\varphi(x),\phi(y))}{\psi(x,y),g(x,y)}-1 $\mid$ \leq\epsilon(x,y)$.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.283-295
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• 2002

In this Paper we show the Solution of the following Jensen functional equation with three variables and prove the stability of this equations in the spirit of Hyers, Ulam, Rassias and Gavruta: (equation omitted).

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.615-628
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• 2018

In this paper, we introduce the pioneering trigintic functional equation. Moreover, we establish the general solution of the trigintic functional equation and prove the Hyers-Ulam sum and product stabilities of the same equation in multi-Banach spaces by employing the fixed point approach.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.73-81
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• 2015

In this paper, we present the general solution of the functional equation $$rf(\frac{x+y+z+w}{s})+rf(\frac{x+y-z-w}{s})+rf(\frac{x-y+z-w}{s})+rf(\frac{x-y-z+w}{s})=tf(x)+tf(y)+tf(z)+tf(w)$$ and improve the Hyers-Ulam stability of the equation.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.265-285
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• 2016

In this paper, we introduce functional equations in G-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete G-normed spaces by using the fixed point method.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.77-89
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• 2012

Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive functional equation (0.1) $f(2x+y)=2f(x)+f(y)$ and of the orthogonally quadratic functional equation (0.2) $2f(\frac{x}{2}+y)+2f(\frac{x}{2}-y)=f(x)+4f(y)$ for all $x$, $y$ with $x{\perp}y$ in orthogonality spaces.