• Kyungpook Mathematical Journal
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• v.49 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.615-622
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• 2009

We solve the automatic continuity problem of an approximate higher derivation on a semisimple Banach algebra and investigate Hyers-Ulam stability for higher derivations.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.113-122
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• 2001

We prove the Hyers-Ulam-Rassias stability of the Jensen's equation in Banach modules over a Banach algebra.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.87-97
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• 2009

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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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.

• East Asian mathematical journal
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• v.35 no.3
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• pp.351-356
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the general quartic functional equation f(5x + y) - 5f(4x + y) + 10f(3x + y) - 10f(2x + y) + 5f(x + y) - f(y) = 0.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.1-14
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• 2019

We prove the generalized Hyers-Ulam-Rassias stability problem of the quadratic functional equation with involution in the fuzzy quasi ${\beta}$-normed space by using the fixed point method.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.411-424
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• 2010

In this paper we consider a generalized form of quadratic functional equations and establish new theorems about the generalized Hyers-Ulam stability of the generalized form of quadratic equations in fuzzy normed spaces.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.5-16
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• 2009

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. 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.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1177-1194
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• 2009

In this paper we establish the general solution of the functional equation f(2x+y)+f(x-2y)=2f(x+y)+2f(x-y)+f(-x)+f(-y) and investigate the Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces. 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.