• 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]).

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.413-421
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• 2003

In this paper, using an idea from the direct method of Hyers and Ulam, we investigate the situations so that the Hyers-Ulam-Rassias stability of the functional equation $g(x^2)\;=\;2xg(x)$ is satisfied.

• 대한수학회보
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• 제46권1호
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• pp.87-97
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• 2009

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

• 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.

• 대한수학회보
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• 제56권3호
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• pp.779-787
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• 2019

In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

• 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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• 제44권1호
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• pp.185-194
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• 2007

In this paper we study the Hyers-Ulam-Rassias stability of the functional equations related to a multiplicative derivation.

• 호남수학학술지
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• 제27권2호
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• pp.211-223
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• 2005

In this paper we study the Hyers-Ulam stability and the superstability of functional equations related to a multiplicative derivation.

• 대한수학회보
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• 제56권3호
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• pp.801-813
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• 2019

In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.569-580
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• 2001

In this paper, we obtain some results on the Hyers-Ulam stability for the family of the functional equation f(xоy) = $H(f(x)^{1/t},f(y)^{1/t}$) (x, $y{\in}S$), where H is a homogeneous function of degree t and о is a square-symmetric operation on the set S.