• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.295-306
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• 2021

The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431-436], we will investigate the stability of the general sextic functional equation.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.389-399
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• 2002

In this paper we solve a quadratic Jensen type functional equation (equation omitted) and prove the stability of this equation.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.447-456
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• 2004

In this paper we investigate the Hyers-Ulam-Rassias stability of a 4-dimensional quadratic functional equation (equation omitted).

• East Asian mathematical journal
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• v.36 no.1
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• pp.35-53
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• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.73-83
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• 2001

In this paper, we solve a Jensen type functional equation and prove the stability of the Jensen type functional equation.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.37-46
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• 2000

We prove the stability of a generalized Cauchy functional equation of the form ; $$f(a_1x+a_2y)=b_1f(x)+b_2f(y)+w.$$ That is, we obtain a partial answer for the open problem which was posed by the Th.M Rassias and J. Tabor on the stability for a generalized functional equation.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.45-50
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• 2000

The modified Hyers-Ulam-Rassias Stability Of the generalized form g(x+p) : $\phi$(x)g(x) for the Gamma functional equation shall be proved. As a consequence we obtain the stability theorems for the gamma functional equation.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.415-422
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• 2004

In this paper, we investigate the Hyers-Ulam stability and the super-stability of the functional equation f(x＋y＋rxy) = f(x)＋f(y)＋rxf(y)＋ryf(x) which is obtained by combining the additive Cauchy functional equation and the derivation functional equation.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.269-275
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• 2021

Let ℝ be the set of real numbers, f, g : ℝ → ℝ and �� ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$f({\sqrt[n]{x^N+y^N}})=f(x)g(y)$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$\|f({\sqrt[n]{x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$ for all x, y ∈ ℝ.