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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 STABILITY OF AN n-DIMENSIONAL QUADRATIC EQUATION
Kil Woung Jun,Sang Baek Lee 충청수학회 2007 충청수학회지 Vol.20 No.1
Let X and Y be vector spaces. In this paper we prove that a mapping f : X ! Y satis¯es the following functional equa- tion X1·k<l·n(f(xk + xl) + f(xk ¡ xl)) ¡ 2(n ¡ 1)Xni=1f(xi) = 0 if and only if the mapping f is quadratic. In addition we investi-gate the generalized Hyers-Ulam-Rassias stability problem for the functional equation.
ON THE STABILITY OF A CUBIC FUNCTIONAL EQUATION
Kil Woung Jun,Yang Hi Lee 충청수학회 2008 충청수학회지 Vol.21 No.3
In this paper, we prove the stability of the functional equation X3 i=0 3Ci(−1)3−if(ix + y) − 3!f(x) = 0 in the sense of P. G˘avruta on the punctured domain. Also, we investigate the superstability of the functional equation.
On the Stability of the Quadratic Equation in Banach Modules over a Banach Algebra
Kil-Woung Jun,Hark-Mahn Kim 경북대학교 자연과학대학 수학과 2004 Kyungpook mathematical journal Vol.44 No.3
We prove the Hyers-Ulam-Rassias stability of quadratic functional equations f(x + y)+ f(x y ) = (1+ 2)(f(x)+ f(y)) and f(x + y)+ f(x y ) = (1+)(f(x)+ f(y)) between Banach modules over a Banach algebra.
ON THE HYERS-ULAM-RASSIAS STABILITY OF A PEXIDERIZED MIXED TYPE QUADRATIC FUNCTIONAL EQUATION
Kil Woung Jun,Gwang Hui Kim,Yang Hi Lee 충청수학회 2007 충청수학회지 Vol.20 No.2
We establish the Hyers-Ulam-Rassias stability of the Pexiderized mixed type quadratic equation f1(x + y + z) + f2(x ¡ y) + f3(x ¡ z) ¡ f4(x ¡ y ¡ z) ¡ f5(x + y) ¡ f6(x + z) = 0 in the spirit of D. H. Hyers, S. M. Ulam and Th. M. Rassias.
GENERALIZED STABILITY OF EULER-LAGRANGE TYPE QUADRATIC MAPPINGS
Kil Woung Jun,Jeong Ha Oh 충청수학회 2007 충청수학회지 Vol.20 No.4
In this paper, we investigate the generalized Hyers{Ulam{Rasssias stability of the following Euler-Lagrange type qua- dratic functional equation f(ax+by+cz)+f(ax+by¡cz)+f(ax¡by + cz) + f(ax ¡ by ¡ cz) = 4a2f(x) + 4b2f(y) + 4c2f(z).
STABILITY OF A GENERALIZED JENSEN TYPE QUADRATIC FUNCTIONAL EQUATIONS
Kil Woung Jun,Young Sun Cho 충청수학회 2007 충청수학회지 Vol.20 No.4
In this paper, we investigate the Hyers{Ulam{Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.
SOLUTION AND STABILITY OF MIXED TYPE FUNCTIONAL EQUATIONS
Kil Woung Jun,Il Sook Jung,Hark Mahn Kim 충청수학회 2009 충청수학회지 Vol.22 No.4
In this paper we establish the general solution of the following functional equation with mixed type of quadratic and additive mappings f(mx + y) + f(mx − y) + 2f(x) = f(x + y) + f(x − y) + 2f(mx), where m 2 is a positive integer, and then investigate the generalized Hyers–Ulam stability of this equation in quasi-Banach spaces.
ON THE HYERS-ULAM-RASSIAS STABILITY OF A CAUCHY-JENSEN FUNCTIONAL EQUATION II
Kil Woung Jun,Ju Ri Lee,Yang Hi Lee 충청수학회 2008 충청수학회지 Vol.21 No.2
In this paper, we obtain the Hyers-Ulam-Rassias stability of a Cauchy-Jensen functional equation f(x + y, z) − f(x, z) − f(y, z) = 0, 2f(x,y + z2) − f(x, y) − f(x, z) = 0in the spirit of Th. M. Rassias.