• The Pure and Applied Mathematics
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• 제19권2호
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• pp.171-177
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• 2012

The main purpose of this paper is to investigate $h$-stability of the nonlinear perturbed differential systems using the notion of $t_{\infty}$-similarity. As results, we generalize some previous $h$-stability results on this topic.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.415-422
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• 2004

In this paper, we investigate the Hyers-Ulam stability and the super-stability of the functional equation f(x＋y＋rxy) = f(x)＋f(y)＋rxf(y)＋ryf(x) which is obtained by combining the additive Cauchy functional equation and the derivation functional equation.

• 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.

• Communications of the Korean Mathematical Society
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• 제32권4호
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• pp.851-864
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• 2017

The problems of global and local exponential stability analysis of a class of nonlinear non-autonomous difference equations in Banach spaces are studied in this paper. By a novel comparison technique, new explicit exponential stability conditions are derived. Numerical examples are given to illustrate the effectiveness of the obtained results.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.91-101
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• 2015

In this paper, we investigate the stability of the functional equation f(-x + y + z + w) + f(x - y + z + w) + f(x + y - z + w) + f(x + y + z - w) = 3f(x) + f(-x) + 3f(y) + f(-y) + 3f(z) + f(-z) + 3f(w) + f(-w) by using the direct method in the sense of Hyers.

• Journal of the Chungcheong Mathematical Society
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• 제31권1호
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• pp.89-101
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• 2018

In this paper, we consider the Hyers-Ulam stability on multi-valued dynamics. For a generalized n-dimensional quadratic set-valued functional equation, we prove the Hyers-Ulam stability for the functional equation in multi-valued dynamics.

• The Pure and Applied Mathematics
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• 제20권3호
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• pp.223-232
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• 2013

Alexseev's formula generalizes the variation of constants formula and permits the study of a nonlinear perturbation of a system with certain stability properties. In recent years M. Pinto introduced the notion of $h$-stability. S.K. Choi et al. investigated $h$-stability for the nonlinear differential systems using the notion of $t_{\infty}$-similarity. Applying these two notions, we study bounds for solutions of the perturbed differential systems.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권3호
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• pp.238-243
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• 2009

This paper present same thodology for the classification of power system voltage stability, the trajectory of which to instability is monotonic, using an interior point method based support vector machine(IPMSVM). The SVM based voltage stability classifier canp rovide real-time stability identification only using the local measurement data, without the topological information conventionally used.

• Honam Mathematical Journal
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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).

• Journal of Electrical Engineering and Technology
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• 제6권5호
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• pp.713-722
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• 2011

In the present paper, the problem of stability analysis for linear systems with interval time-varying delays is considered. By introducing a new Lyapunov-Krasovskii functional, new stability criteria are derived in terms of linear matrix inequalities (LMIs). Two numerical examples are given to show the superiority of the proposed method.