• 충청수학회지
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• 제31권4호
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• pp.397-409
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• 2018

In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation $$f\({\sum\limits_{i=1}^{n}}x_i\)+{\sum\limits_{1{\leq}i<j{\leq}n}}f(x_i-x_j)-n{\sum\limits_{i=1}^{n}f(x_i)=0$$ for integer values of n such that $n{\geq}2$, where f is a mapping from a vector space V to a Banach space Y.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권2호
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• pp.189-199
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• 2022

In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

• 대한수학회보
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• 제44권4호
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• pp.825-840
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• 2007

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• 충청수학회지
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• 제21권3호
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• pp.377-384
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• 2008

In this paper, we prove the stability of the functional equation $$\sum\limits_{i=0}^{3}3Ci(-1)^{3-i}f(ix+y)-3!f(x)=0$$ in the sense of P. $G{\breve{a}}vruta$ on the punctured domain. Also, we investigate the superstability of the functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권2호
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• pp.111-125
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• 2007

For an odd mapping, we study a generalized additive functional equation in Banach spaces and Banach modules over a $C^*-algebra$. And we obtain generalized solutions of a generalized additive functional equation and so generalize the Cauchy-Rassias stability.

• 대한수학회보
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• 제45권2호
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• pp.397-403
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• 2008

In this paper, we modify L. $C\breve{a}dariu$ and V. Radu's result for the stability of the monomial functional equation $\sum\limits_{n=0}^{n}n\;C_i(-1)^{n-i}f(ix+y)-n!f(x)=0$ in the sense of Th. M. Rassias. Also, we investigate the superstability of the monomial functional equation.

• 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.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.159-168
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• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k²f(x + y) - k²f(x - y) + 2(k² - 1)f(x) + (k² + k³)f(y) + (k² - k³)f(-y) - 2f(ky) = 0.

• 대한수학회보
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• 제34권4호
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• pp.561-571
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• 1997

The general (continuous) solution and the asymptotic behaviors of the unbounded solution of the functional equation $f(x + y)^2 = af(x)f(y) + bf(x)^2 + cf(y)^2$ and the Hyers-Ulam stability of that functional equation for the case when a = 2 and b = c = 1 shall be investigated.

• 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.