• 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.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.295-306
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• 2024

In this work, we investigate the generalized Hyers-Ulam stability of quadratic functional inequality in modular spaces satisfying ∆₂-conditions and Fatou property, and in 𝛽-homogeneous Banach spaces.

• Korean Journal of Mathematics
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• 제17권1호
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• pp.91-102
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• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the 3-variable Cauchy functional equation.

• 대한수학회보
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• 제38권2호
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• pp.261-272
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• 2001

In this paper we prove the stability of the generalized quadratic equation f(x+y)+g(x-y)-2f(x)-2g(y)=0 in the spirit of Hyers, Ulam and Rassias.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.67-79
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• 2009

We establish the generalized Hyers-Ulam-Rassias stability of higher ring derivations. Furthermore, we use the superstability of higher ring derivations to obtain approximately higher linear derivations mapping into the Jacobson radical under some conditions.

• 대한수학회보
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• 제46권1호
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• pp.11-23
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• 2009

In this paper, we prove the generalized Hyers-Ulam stability of the functional inequalities associated with additive functional mappings. Also, we find the solution of these inequalities which satisfy certain conditions.

• 충청수학회지
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• 제28권2호
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• pp.311-319
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• 2015

In this article, we consider a modified quadratic functional equation and then investigate its generalized Hyers-Ulam stability theorem in quasi-${\beta}$-normed spaces.

• 호남수학학술지
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• 제29권1호
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• pp.61-74
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• 2007

Th. M. Rassias obtained the Hyers-Ulam stability of the general Euler-Lagrange functional equation. In this paper we prove the stability of generlized Euler-Lagrange functional equations in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruta.

• 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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• 제24권2호
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• pp.221-238
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• 2011

We prove the Hyers-Ulam stability of generalized Jensen's equations in Banach modules over a unital $C^{\ast}$-algebra. It is applied to show the stability of generalized Jensen's equations in a Hilbert module over a unital $C^{\ast}$-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital $C^{\ast}$-algebra.