• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권3호
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• pp.237-247
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• 2006

In this paper we solve the Hyers-Ulam stability problem for quadratic functional equations on restricted domains, and then obtain an asymptotic behavior of quadratic mappings on restricted domains.

• 충청수학회지
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• 제28권2호
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• pp.311-319
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• 2015

In this article, we consider a modified quadratic functional equation and then investigate its generalized Hyers-Ulam stability theorem in quasi-${\beta}$-normed spaces.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.133-144
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• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• 충청수학회지
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• 제23권3호
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• pp.411-424
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• 2010

In this paper we consider a generalized form of quadratic functional equations and establish new theorems about the generalized Hyers-Ulam stability of the generalized form of quadratic equations in fuzzy normed spaces.

• 충청수학회지
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• 제37권2호
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• pp.87-97
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• 2024

For any fixed integers k, l with kl(l - 1) ≠ 0, we establish the generalized Hyers-Ulam stability of an Euler-Lagrange quadratic functional equation f(kx + ly) + f(kx - ly) + 2(l - 1)[k²f(x) - lf(y)] = l[f(kx + y) + f(kx - y)] in normed spaces and in non-Archimedean spaces, respectively.

• 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.

• 충청수학회지
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• 제20권4호
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• pp.535-542
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• 2007

In this paper, we investigate the generalized Hyers-Ulam{Rasssias stability of the following Euler-Lagrange type quadratic functional equation $$f(ax+by+cz)+f(ax+by-cz)+f(ax-by+cz)+f(ax-by-cz)=4a^2f(x)+4b^2f(y)+4c^2f(z)$$.

• East Asian mathematical journal
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• 제32권3호
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• pp.413-423
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• 2016

In this paper, we consider the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy Banach space. The usual method to obtain the stability for mixed type functional equation is to split the cases according to whether the involving mappings are odd or even. In this paper, we show that the stability of a quadratic-cubic mapping can be obtained without distinguishing the two cases.

• 대한수학회보
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• 제49권2호
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• pp.339-352
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• 2012

We prove the stability for the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients on the probabilistic normed spaces (briefly PN spaces).

• 충청수학회지
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• 제22권4호
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• pp.815-830
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• 2009

In this paper we establish the general solution of the following functional equation with mixed type of quadratic and additive mappings f(mx+y)+f(mx-y)+2f(x)=f(x+y)+f(x-y)+2f(mx), where $m{\geq}2$ is a positive integer, and then investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.