• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.569-587
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• 2007

In this paper, we establish the generalized Hyers-Ulam-Rassias stability of the Pexider type quadratic equation $f_1(x+y+z)+f_2(x-y)+f_3(x-z)-f_4(x-y-z)-f_5(x+y)-f_6(x+z)=0$ and its general solution.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.907-913
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• 2013

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(2x_1)+f(2x_2)+{\cdots}+f(2x_n){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that 2${\leq}$t

• Honam Mathematical Journal
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• v.39 no.3
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• pp.417-430
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• 2017

In this paper, we investigate the stability of a functional equation $$2f(ax+by)+abf(x-y)+abf(y-x)-{\frac{2af((a+b)x)}{a+b}}-{\frac{bf((a+b)y)}{a+b}}-{\frac{bf(-(a+b)y)}{a+b}}=o$$ by applying the direct method in the sense of Hyers and Ulam.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.29-43
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• 2010

In this note, by using the fixed point method, we prove the generalized stability for a mixed type functional equation in random normed spaces of which the general solution is either cubic or quadratic.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.587-600
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• 2016

We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+{\frac{1}{2}}a(a^2+1)f(x-y)+(a^4-1)f(y)={\frac{1}{2}}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie ${\ast}$-derivation by using a directed method and an alternative fixed point method.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2061-2070
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• 2013

In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.499-507
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• 2006

In this paper, we obtain the general solution and the stability of the hi-Jensen functional equation $$4f(\frac {x+y} 2,\;\frac {z+w} 2)=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.347-357
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• 2004

In this note we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the cubic functional equation f(3$\chi$+y) + f($3\chi$-y) = $3f(\chi$+ y) + $3f(\chi$-y) + ($48f(\chi)$ on abelian groups.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.9
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• pp.670-677
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• 1987

The robustness and stability properties for a model reference adaptive control system with plant uncertainty are considered in this paper, using input-output stability theory. An error model for a typical adaptive control structure is extended to unmodelled dynamics in the plant model and then, the strictly positive real condition for global stability is examined. In general, since this condition can be easily violated due to unmodelled dynamics, a modified compensator which can be guaranteed Hev e SPR is introduced in the plant model and the effectiveness for the given structure is also given.