• 한국지능시스템학회논문지
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• 제11권8호
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• pp.726-730
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• 2001

본 논문은 E$^{2}$$_{N}$상의 비선형 퍼지 중성 미분방정식의 관측가능성에 대해 연구하였다.

• 대한수학회논문집
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• 제20권2호
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• pp.321-338
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• 2005

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))\;=\;\phi(X)f(X)$, where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and Gavruta for many other equations such as the gamma, beta, Schroder, iterative, and G-function type's equations.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.53-63
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• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• 충청수학회지
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• 제35권4호
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• pp.315-327
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• 2022

In this paper, we investigate the transferred superstability for the p-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from the p-radical functional equations: $$f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)g(y),\;\\f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)h(y),$$ where p is an odd positive integer, λ is a positive real number, and f is a complex valued function. Furthermore, the results are extended to Banach algebras. Therefore, the obtained result will be forced to the pre-results(p=1) for this type's equations, and will serve as a sample to apply it to the extension of the other known equations.

• 충청수학회지
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• 제17권1호
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• pp.29-45
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• 2004

We prove the Cauchy-Rassias stability of cyclic functional equations in Banach modules over a unital $C^*$-algebra.

• 충청수학회지
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• 제20권4호
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• pp.515-523
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• 2007

In this paper, we investigate the Hyers-Ulam-Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.

• 대한수학회논문집
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• 제23권4호
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• pp.567-575
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• 2008

In this article we prove the Hyers.Ulam stability of trigonometric functional equations.

• 대한수학회보
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• 제44권2호
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• pp.315-330
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• 2007

In this paper, some hybrid fixed point theorems are proved which are further applied to first and second order neutral functional differential equations for proving the existence results for the extremal solutions under the mixed Lipschitz, compactness and monotonic conditions.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.929-935
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• 1999

By applications of the stability for a class of functional equa-tions we obtain the hyers-Ulam stability for the equations of the form g($\chi$+y)=kg($\chi$)g(y) in the following setting; ｜g($\chi$+y)-kg($\chi$)g(y)｜$\leq$$\Delta$($\chi$,y).

• 충청수학회지
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• 제22권1호
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• pp.31-37
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• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a functional equation and a system of functional equations on Jensen-quadratic mappings.