• East Asian mathematical journal
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• 제35권3호
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• pp.351-356
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the general quartic functional equation f(5x + y) - 5f(4x + y) + 10f(3x + y) - 10f(2x + y) + 5f(x + y) - f(y) = 0.

• 호남수학학술지
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• 제46권1호
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• pp.146-167
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• 2024

In this paper, we investigate the stability of the general decic functional equation $$\sum_{i=0}^{11}_{11}C_i(-1)^{11-i}f(x+iy)=0$$ in the sense of Rassias.

• 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.

• 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.

• East Asian mathematical journal
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• 제35권3호
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• pp.331-340
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• 2019

In this paper, we investigate the stability for the functional equation $f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-(k^3-k)f(y)+(k^3-k)f(-y)=0$ in the sense of M. S. Moslehian and Th. M. Rassias.

• 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.

• 대한수학회보
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• 제41권4호
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• pp.665-676
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• 2004

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.

• 충청수학회지
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• 제34권3호
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• pp.295-306
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• 2021

The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431-436], we will investigate the stability of the general sextic functional equation.

• 대한수학회보
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• 제34권3호
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• pp.437-446
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• 1997

In this paper, the Hyers-Ulam stability and the general Hyers-Ulam stability (more precisely, modified Hyers-Ulam-Rassias stability) of the gamma functional equation (3) in the following setings $$ \left$\mid$ f(x + 1) - xf(x) \right$\mid$ \leq \delta and \left$\mid$ \frac{xf(x)}{f(x + 1)} - 1 \right$\mid$ \leq \frac{x^{1+\varepsilon}{\delta} $$ shall be proved.

• 대한기계학회논문집A
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• 제26권6호
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• pp.1035-1046
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• 2002

Time Delay Control(TDC) is a robust nonlinear control scheme using Time Delay Estimation(TDE) and also has a simple structure. To apply TDC to a real system, we must design Time Delay Controller to guarantee stability. The earlier research stated sufficient stability condition of TDC for general plants. In that research, it was assumed that time delay is infinitely small. But, it is impossible to implement infinitely small time delay in a real system. So, in this research we propose a new sufficient stability condition of TDC for general plants with finite time delay. And the simulation results indicate that the previous sufficient stability condition does not work even for small time delay, while our proposed condition works well.