• East Asian mathematical journal
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• 제36권1호
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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.

• 충청수학회지
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• 제33권2호
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• pp.205-217
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• 2020

We will introduce a new type of quartic functional equation and then investigate the stability for a quartic functional equation in a convex modular space.

• 대한수학회보
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• 제40권4호
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• pp.565-576
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• 2003

In this paper, we determine the general solution of the quartic equation f(x+2y)+f(x-2y)+6f(x) = 4[f(x+y)+f(x-y)+6f(y)] for all x, $y\;\in\;\mathbb{R}$ without assuming any regularity conditions on the unknown function f. The method used for solving this quartic functional equation is elementary but exploits an important result due to M. Hosszu [3]. The solution of this functional equation is also determined in certain commutative groups using two important results due to L. Szekelyhidi [5].

• 대한수학회보
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• 제52권6호
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• pp.1759-1776
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• 2015

We determine the general solution of the generalized additive-quartic functional equation f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) - 13 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.373-388
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• 2010

We introduce mixed cubic-quartic functional equations. And using the fixed point method, we prove the generalized Hyers-Ulam stability of cubic-quartic functional equations on random normed spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권4호
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• pp.247-254
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation f(x + ky) - k²f(x + y) + 2(k² - 1)f(x) - k²f(x - y) + f(x - ky) - k²(k² - 1)(f(y) + f(-y)) = 0, where k is a fixed real number with |k| ≠ 0, 1.

• 충청수학회지
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• 제28권4호
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• pp.635-645
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• 2015

We will show the general solution of the functional equation $$\begin{eqnarray}f(x+ay)+f(x-ay)+2(a^2-1)f(x)\\=a^2f(x+y)+a^2f(x-y)+2a^2(a^2-1)f(y)\end{eqnarray}$$ and investigate the Hyers-Ulam stability of the quartic set-valued functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권4호
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• pp.267-276
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• 2019

In this paper, we investigate the stability of an additive-cubic-quartic functional equation f(x + 2y) - 4f(x + y) + 6f(x) - 4f(x - y) + f(x - 2y) - 12f(y) - 12f(-y) = 0 by applying the fixed point theory in the sense of L. Cădariu and V. Radu.

• 충청수학회지
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• 제33권1호
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• pp.77-87
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• 2020

In this paper, we investigate the stability of a functional equation f(x + 3y) - 5f(x + 2y) + 10f(x + y) - 8f(x) + 5f(x - y) - f(x - 2y) - 2f(-x) - f(2x) + f(-2x) = 0 by using the fixed point theory in the sense of L. Cǎdariu and V. Radu.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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• pp.153-161
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• 2008

In the present paper we introduce a Jensen type quartic functional equation and then investigate the generalized Hyers-Ulam stability problem for the equation.