• 충청수학회지
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• 제21권1호
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• pp.1-14
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• 2008

In this paper, we prove the Hyers-Ulam-Rassias stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and of the Jensen functional equation $2f(\frac{x+y}{2})=f(x)+f(y)$ over the p-adic field ${\mathbb{Q}}_p$. The concept of Hyers-Ulam-Rassias stability originated from the 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.

• 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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• 제43권1호
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• pp.107-117
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• 2006

We give some necessary and sufficient conditions in order that a closed operator in a Hilbert space into another have the Hyers-Ulam stability. Moreover, we prove the existence of the stability constant for a closed operator. We also determine the stability constant in terms of the lower bound.

• 충청수학회지
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• 제31권2호
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• pp.199-230
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• 2018

In this paper, we introduce the general form of a viginti functional equation. Then, we find the general solution and study the generalized Ulam-Hyers stability of such functional equation in multi-Banach spaces by using fixed point technique. Also, we indicate an example for non-stability case regarding to this new functional equation.

• 충청수학회지
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• 제22권3호
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• pp.383-398
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• 2009

In this paper, we study the generalized Hyers-Ulam stability of a bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,w)+f(y,\;z)+f(y,w)$$. Moreover, we establish stability results on the punctured domain.

• 충청수학회지
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• 제30권1호
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• pp.141-149
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• 2017

In this article, we consider the Hyers-Ulam stability in multi-valued dynamics. We prove the Hyers-Ulam stability for a cubic set-valued functional equation on multi-valued dynamics by using several methods.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.429-445
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• 2004

In this paper we investigate the generalized Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(x,y)){\;}={\;}\phi(x,y)f(x,y)$, where x, y lie in the set S. As a consequence we obtain stability in the sense of Hyers, Ulam, Rassias, Gavruta, for some well-known equations such as the gamma, beta and G-function type equations.

• 충청수학회지
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• 제21권2호
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• pp.165-174
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• 2008

In this paper, we obtain the general solution, the generalized Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a cubic functional equation $4f(x+my)+4f(x-my)+m^2f(2x)=8f(x)+4m^2f(x+y)+4m^2f(x-y)$ for a positive integer $m{\geq}2$.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.671-684
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• 2023

In this paper, we prove the generalized Hyers-Ulam stability of a general quintic functional equation, $\sum\limits_{k=0}^{6}(-1)^k{_6}C_kf(x+(3-k)y)=0$, by using the fixed point method.

• 충청수학회지
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• 제23권2호
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• pp.335-348
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• 2010

In this paper, we study the Hyers-Ulam-Rassias stability of a bi-Pexider functional equation $$f(x+y,z)-f_1(x,z)-f_2(y,z)=0$$, $$f(x,y+z)-f_3(x,y)-f_4(x,z)=0$$. Moreover, we establish stability results on the punctured domain.