• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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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.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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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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• v.60 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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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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• v.32 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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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).

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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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.