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On the stability of an n-dimensional quadratic equation
전길웅,이상백 충청수학회 2007 충청수학회지 Vol.20 No.1
LetX and Y be vector spaces. In this paper we provethat a mapping f :X ! Y satises the following functional equa-tionX1 k<l n(f(xk + xl) + f(xk xl)) 2(n 1)nXi=1f(xi) = 0if and only if the mapping f is quadratic. In addition we investi-gate the generalized Hyers-Ulam-Rassias stability problem for thefunctional equation.
A generalization of the Hyers-Ulam-Rassias stability of a functional equation of Davison
전길웅,Soon-Mo Jung,Yang-Hi Lee 대한수학회 2004 대한수학회지 Vol.41 No.3
We prove the Hyers-Ulam-Rassias stability of the Davison functional equation f(xy) + f(x + y) = f(xy + x) + f(y) for a class of functions from a ring into a Banach space and we also investigate the Davison equation of Pexider type.
Stability of isometries on Hilbert spaces
전길웅,박달원 대한수학회 2002 대한수학회보 Vol.39 No.1
Let X and Y be real Banach spaces and epsilon, pge 0. A mapping T between X and Y is called an (epsilon,p)-isometry if ||T(x)-T(y)|-|x-y| | le epsilon |x-y|^pfor x, y in X. Let H be a real Hilbert space and T:H to Han (epsilon, p)-isometry with T(0)=0. If p neq 1 is anonnegative number, then there exists a unique isometry I:Hto Hsuch that |T(x)-I(x)| le C(epsilon)(|x|^{(1+p)/2}+|x|^p)for all x in H, where C(epsilon)to 0 as epsilon to 0.
On the generalized Hyers--Ulam stability of a cubic functional equation
전길웅,이상백 충청수학회 2006 충청수학회지 Vol.19 No.2
The generalized Hyers--Ulam stability problems of the cubic functional equation \begin{eqnarray*} &&f(x+y+z)+f(x+y-z)+2f(x-y)+4f(y)\\ &&\qquad =f(x-y+z)+f(x-y-z)\\ && \qquad\qquad +2f(x+y)+2f(y+z)+2f(y-z) \end{eqnarray*} shall be treated under the approximately odd condition and the behavior of the cubic mappings and the additive mappings shall be investigated. The generalized Hyers--Ulam stability problem for functional equations had been posed by Th.M. Rassias and J. Tabor \cite{RT92} in 1992.
ON THE GENERALIZED HYERS-ULAM STABILITY OF THE CAUCHY-JENSEN FUNCTIONAL EQUATION II
전길웅,이주리,이양희 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.2
In this paper, we obtain the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation f(x + y, z) - f(x, z) - f(y, z) = 0, 2f x, y + z/2 -f(x, y) - f(x,z) = 0 in the spirit of P. Gavruta.
위상수학에 관한 연구 : 리이만다양체에서의 임계사상에 관하여 On the Critical Mappings of the Riemannian Manifolds
전길웅,강명경 충남대학교 자연과학연구소 1982 忠南科學硏究誌 Vol.9 No.1
There are many defined functional on the space of smooth maps of one Riemannian manifold to another. Maps that are critical for every defined functional are called critical. This paper shows that the fibers of critical maps are minimal submanifolds. Also, it provides a characterization of hypercritical maps and shows that the inverse of the hypercritical map is hypercritical.
On the Hyers-Ulam-Rassias stability of a Pexiderized mixed type quadratic functional equation
전길웅,김광휘,이양희 충청수학회 2007 충청수학회지 Vol.20 No.2
We establish the Hyers-Ulam-Rassias stability of the Pexiderized mixed 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 $ in the spirit of D. H. Hyers, S. M. Ulam and Th. M. Rassias.
The range of derivations on Banach algebras
전길웅,김학만 대한수학회 2002 대한수학회보 Vol.39 No.2
In this paper we show that if D is a continuous linearJordan derivation on a Banach algebra A satisfying[[D(x^{n}), x^{n}], x^{n}] in rad(A) for a positive integern and for all x in A, then D maps A into rad(A).
On the Hyers-Ulam stability of a generalized quadratic and additive functional equation
전길웅,김학만 대한수학회 2005 대한수학회보 Vol.42 No.1
In this paper, we obtain the general solution of a generalizedquadratic and additive type functional equationbegin{eqnarray}nonumberf(x+ay)+a f(x-y)=f(x-ay)+a f(x+y)end{eqnarray}for any integer a with a neq -1,0,1 in the class of functionsbetween real vector spaces and investigate the generalizedHyers-Ulam stability problem for the equation.