• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.929-935
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• 1999

By applications of the stability for a class of functional equa-tions we obtain the hyers-Ulam stability for the equations of the form g($\chi$+y)=kg($\chi$)g(y) in the following setting; ｜g($\chi$+y)-kg($\chi$)g(y)｜$\leq$$\Delta$($\chi$,y).

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.65-80
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• 2010

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.315-327
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• 2010

We give a xed point approach to the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x) in non-Archimedean normed spaces. We will give an example to show that some known results in the stability of cubic functional equations in real normed spaces fail in non-Archimedean normed spaces. Finally, some applications of our results in non-Archimedean normed spaces over p-adic numbers will be exhibited.

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.237-247
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• 2006

In this paper we solve the Hyers-Ulam stability problem for quadratic functional equations on restricted domains, and then obtain an asymptotic behavior of quadratic mappings on restricted domains.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.31-37
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• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a functional equation and a system of functional equations on Jensen-quadratic mappings.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.509-524
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• 2023

In this study, we characterize the structure of the multivariable mappings which are sextic in each component. Indeed, we unify the general system of multi-sextic functional equations defining a multi-sextic mapping to a single equation. We also establish the Hyers-Ulam and Găvruţa stability of multi-sextic mappings by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability results in the setting of quasi-𝛽-normed spaces. Using a characterization result, we indicate an example for the case that a multi-sextic mapping is non-stable.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.53-61
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• 2003

We prove the generalized Hyers-Ulam-Rassias stability of the invertible mapping in a Banach module over a unital Banach algebra, and prove the generalized Hyers-Ulam-Rassias stability of the Jensen's functional equations in a Hilbert module over a unital $C^{*}$-algebra.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.219-227
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• 2018

In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.243-251
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• 2017

In this paper, we solve the additive ${\rho}-functional$ equations (0.1) $f(x+y)+f(x-y)-2f(x)={\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x))$, and (0.2) $2f(\frac{x+y}{2})+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$, where ${\rho}$ is a fixed (complex) number with ${\rho}{\neq}1$, Using the direct method, we prove the Hyers-Ulam stability of the additive ${\rho}-functional$ equations (0.1) and (0.2) in ${\beta}-homogeneous$ (complex) F-spaces.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.801-812
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• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.