• East Asian mathematical journal
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• 제35권3호
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• pp.331-340
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• 2019

In this paper, we investigate the stability for the functional equation $f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-(k^3-k)f(y)+(k^3-k)f(-y)=0$ in the sense of M. S. Moslehian and Th. M. Rassias.

• 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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• 제34권3호
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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.

• 호남수학학술지
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• 제32권1호
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• pp.29-43
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• 2010

In this note, by using the fixed point method, we prove the generalized stability for a mixed type functional equation in random normed spaces of which the general solution is either cubic or quadratic.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.291-305
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• 2018

In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

• 대한수학회보
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• 제41권2호
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• pp.347-357
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• 2004

In this note we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the cubic functional equation f(3$\chi$+y) + f($3\chi$-y) = $3f(\chi$+ y) + $3f(\chi$-y) + ($48f(\chi)$ on abelian groups.