• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.89-101
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• 2018

In this paper, we consider the Hyers-Ulam stability on multi-valued dynamics. For a generalized n-dimensional quadratic set-valued functional equation, we prove the Hyers-Ulam stability for the functional equation in multi-valued dynamics.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.27-36
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• 2006

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. We introduce the concept of linear ${\theta}$-derivations on $JB^*$-triples, and prove the Cauchy-Rassias stability of linear ${\theta}$-derivations on $JB^*$-triples.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.17.2-17
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• 2003

The purpose of this paper is to solve the generalized Hyers-Ulam stability problem for a cubic functional equation 8f(x-y/2)＋8f(y-x/2)＋2f(x＋y)=9f(x)＋9f(y) on the basis of a direct method.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.25-33
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• 2002

We prove the generalized Hyers-Ulam-Rassias stability of linear operators in a Hilbert module over a unital $C^*$-algebra.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.415-426
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• 2020

In this paper, we will prove some uniqueness theorems that can be applied to the generalized Hyers-Ulam stability of some additive-quadratic-cubic functional equation in complete modular spaces without Δ₂-conditions.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.371-381
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• 2011

We establish alternative stability and superstability of $J^{\ast}$-derivations in $J^{\ast}$-algebras for a generalized Jensen type functional equation by using the direct method and the fixed point alternative method.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2002.09a
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• pp.22.1-22
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• 2002

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.1
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• pp.13-19
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• 1995

In this paper, generalized singular value is defined. Using the generalized singular value, robust stability conditions and robust pole placement conditions of structured uncertain systems with star shaped uncertainties are derived. Especially, norm bounded and polytopic uncertainty regions are considered as star shaped uncertainty regions. Linear matrix inequality problems are proposed in order to compute the upper bound of the generalized singular value. The proposed linear matrix inequality problems can be solved by using the convex optimization method.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.569-587
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• 2007

In this paper, we establish the generalized Hyers-Ulam-Rassias stability of the Pexider type quadratic equation $f_1(x+y+z)+f_2(x-y)+f_3(x-z)-f_4(x-y-z)-f_5(x+y)-f_6(x+z)=0$ and its general solution.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.397-407
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• 2012

Let X and Y be vector spaces. We introduce a new type of a cubic functional equation $f$ : $X{\rightarrow}Y$. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.