• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권4호
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• pp.313-328
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• 2011

We investigate the stability of the functional equation f(x+y+z+w)+2f(x)+2f(y)+2f(z)+2f(w)-f(x+y)-f(x+z)-f(x+w)-f(y+z)-f(y+w)-f(z+w)=0 by using a flxed point theorem in the sense of L. C$\breve{a}$adariu and V. Radu.

• 충청수학회지
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• 제32권1호
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• pp.113-125
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• 2019

In this paper, I investigate the stability of the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.343-355
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• 2019

In this paper, we investigate the stability of the functional equation $$f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-f(ky)+{\frac{k^3+k^2-2k}{2}}f(-y)-{\frac{k^3-k^2-2k}{2}}f(y)=0$$ by using the fixed point theory in the sense of L. $C{\breve{a}}dariu$ and V. Radu.

• 호남수학학술지
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• 제41권2호
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• pp.369-380
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• 2019

Inspired by the problem of finding hyperelastic curves in a Riemannian manifold, we present a study on the variational problem of a hyperelastic curve in Lie group. In a Riemannian manifold, we reorganize the characterization of the hyperelastic curve with appropriate constraints. By using this equilibrium equation, we derive an Euler-Lagrange equation for the hyperelastic energy functional defined in a Lie group G equipped with bi-invariant Riemannian metric. Then, we give a solution of this equation for a null hyperelastic Lie quadratic when Lie group G is SO(3).

• 호남수학학술지
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• 제41권2호
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• pp.391-402
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• 2019

In this paper, I prove the stability of the following set-valued functional equation $$f(x+2y){\oplus}f(x-2y){\oplus}3f(2x){\oplus}f(-2x)\\{\hspace{100}}=4f(x+y){\oplus}4f(x-y){\oplus}10f(x)$$ by employing the direct method in the sense of Hyers and Ulam.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권2호
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• pp.115-130
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• 2010

Let $\cal{A}$ be a unital Banach algebra. If f : $\cal{A}{\rightarrow}\cal{A}$ is an approximately quadratic derivation in the sense of Hyers-Ulam-J.M. Rassias, then f : $\cal{A}{\rightarrow}\cal{A}$ is anexactly quadratic derivation. On the other hands, let $\cal{A}$ and $\cal{B}$ be Banach algebras.Any approximately generalized homomorphism f : $\cal{A}{\rightarrow}\cal{B}$ corresponding to Cauchy, Jensen functional equation can be estimated by a generalized homomorphism.

• 충청수학회지
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• 제22권1호
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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.

• 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.

• 충청수학회지
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• 제32권1호
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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.

• East Asian mathematical journal
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• 제28권5호
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• pp.587-595
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• 2012

In this paper we consider the quadratic matrix equation which can be defined be $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix; A,B and C are $n{\times}n$ given matrices with real elements. Newton's method is considered to find the skew-symmetric solvent of the nonlinear matrix equations Q(X). We also show that the method converges the skew-symmetric solvent even if the Fr$\acute{e}$chet derivative is singular. Finally, we give some numerical examples.