• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.561-567
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• 2001

In this paper, we investigate the Hyers-Ulam-Rassias stability of a quadratic functional equation f(x+y+z)+f(x-y)+f(y-z)+f(x-z) = 3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam stability of the equation on bounded domains.

• 대한수학회보
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• 제52권2호
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• pp.685-697
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• 2015

We investigate the stability of nonlinear differential equations of the form $y^{(n)}(x)=F(x,y(x),y^{\prime}(x),{\cdots},y^{(n-1)}(x))$ with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.

• 대한수학회논문집
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• 제16권2호
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• pp.211-223
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• 2001

In this paper, we obtain the modified Hyers-Ulam-Rassias stability for the family of the functional equation f(x o y) = H(f(x)(sup)1/t, f(y)(sup)1/t)(x,y) $\in$S), where H is a s homogeneous function of degree t and o is a square-symmetric operation on the set S.

• 대한수학회보
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• 제38권2호
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• pp.325-336
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• 2001

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of a quadratic function equation f(x+y+z)+f(x-y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam-Rassias stability of the equation on bounded domain.

• 충청수학회지
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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.

• 대한수학회지
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• 제38권3호
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• pp.645-656
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• 2001

In this paper, we will prove the Hyers-Ulam stability of the quadratic functional equation of Pexider type, f$_1$(x+y) + F$_2$(x-y) = f$_3$(x) + f$_4$(y).

• 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.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.471-477
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• 2003

In this paper we invstigate the new additive type functional equation f(2x - y) + f(x-2y) = 3f(x)-3f(y) and prove the stability problem for this equation in the spirit of Hyers, Ulam, Rassias and Gavruta.

• 충청수학회지
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• 제29권1호
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• pp.83-93
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• 2016

In this paper, we introduce a generalized quadratic functional equation with several variables and then investigate its generalized Hyers-Ulam stability in normed spaces.

• 대한수학회보
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• 제33권4호
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• pp.513-519
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• 1996

The stability problem of functional equations has been originally raised by S. M. Ulam. In 1940, he posed the following problem: Give conditions in order for a linear mapping near an approximately additive mapping to exist (see [9]).