• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2212-2214
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• 2004

Robust stable analysis with the system bounded parameteric variation is very important among the various control theory. This study is to investigate the robust stable conditions using the quadratic form Lyapunov function in which the coefficient matrix is affined linear system. The quadratic stability using the quadratic form Lyapunov function is not investigated yet. The Lyapunov unction is robust stable not to be dependent by the variable parameters, which means that the Lyapunov function is conservative. We suggest the robust stable conditions in the Lyapunov function in which the variable parameters are dependent in order to reduce the conservativeness of quadratic stability.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1421-1433
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• 2011

In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.987-996
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• 2010

In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation: $$f(\frac{sx+ty}{2}+rz)+f(\frac{sx+ty}{2}-rz)+f(\frac{sx-ty}{2}+rz)+f(\frac{sx-ty}{2}-rz)=s^2f(x)+t^2f(y)+4r^2f(z)$$ for any fixed nonzero integers s, t, r with $r\;{\neq}\;{\pm}1$.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.171-182
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• 2012

In this paper, for any fixed integer $n\;>\;m\;{\geq}\;1$, we investigate the generalized Hyers-Ulam stability of the following quadratic functional equation $f(nx+my)\;+\;f(nx-my)\;=\;mn[f(x+y)\;+\;f(x-y)]\;+\;2(n-m)[nf(x)\;-\;mf(y)]$ in ${p}$-Banach spaces, where $0\;<\;p\;{\leq}\;1$. And we prove the same stability of the above functional equation in 2-Banach spaces.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.65-80
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• 2010

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.115-130
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• 2010

Let $\cal{A}$ be a unital Banach algebra. If f : $\cal{A}{\rightarrow}\cal{A}$ is an approximately quadratic derivation in the sense of Hyers-Ulam-J.M. Rassias, then f : $\cal{A}{\rightarrow}\cal{A}$ is anexactly quadratic derivation. On the other hands, let $\cal{A}$ and $\cal{B}$ be Banach algebras.Any approximately generalized homomorphism f : $\cal{A}{\rightarrow}\cal{B}$ corresponding to Cauchy, Jensen functional equation can be estimated by a generalized homomorphism.

• 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.

• 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 $k{\neq}-1$.

• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.5
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• pp.651-655
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• 2018

In this paper, based on an augmented Lyapunov-Krasovskii functional(LKF) with time-delay product quadratic terms, the stability result in the form of linear matrix inequality(LMI) is proposed. In getting an LMI result, the free matrix based integral inequality is used. Finally, two well-known numerical examples are given to demonstrate the usefulness of the proposed result.