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Korean Journal of Mathematics
Journal Basic Information
pISSN :
19768605
eISSN :
22881433
Journal DOI :
10.11568/kjm
Frequency :
Others
Publisher:
The KangwonKyungki Mathematical Society
Editor in Chief :
GiSang Cheon
Volume & Issues
Volume 19, Issue 4  Dec 2011
Volume 19, Issue 3  Sep 2011
Volume 19, Issue 2  Jun 2011
Volume 19, Issue 1  Mar 2011
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1
ON A CERTAIN CLASS OF pVALENT UNIFORMLY CONVEX FUNCTIONS USING DIFFERENTIAL OPERATOR
Lee, S.K. ; Khairnar, S.M. ; Rajas, S.M. ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 1~16
DOI : 10.11568/kjm.2011.19.1.001
Abstract
In this paper, using differential operator, we have introduce new class of pvalent uniformly convex functions in the unit disc U = {z : z < 1} and obtain the coefficient bounds, extreme bounds and radius of starlikeness for the functions belonging to this generalized class. Furthermore, partial sums
of functions
in the class
are considered. The various results obtained in this paper are sharp.
2
GENERALIZED QUADRATIC MAPPINGS IN 2d VARIABLES
Cho, Yeol Je ; Lee, Sang Han ; Park, Choonkil ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 17~24
DOI : 10.11568/kjm.2011.19.1.017
Abstract
Let X, Y be vector spaces. It is shown that if an even mapping
satisfies f(0) = 0, and
for all
,
,
, then the even mapping
is quadratic. Furthermore, we prove the HyersUlam stability of the above functional equation in Banach spaces.
3
ON THE ES CURVATURE TENSOR IN g  ESX
_{n}
Hwang, In Ho ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 25~32
DOI : 10.11568/kjm.2011.19.1.025
Abstract
This paper is a direct continuation of [1]. In this paper we investigate some properties of EScurvature tensor of g 
, with main emphasis on the derivation of several useful generalized identities involving it. In this subsequent paper, we are concerned with contracted curvature tensors of g 
and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in g 
, which has a great deal of useful physical applications.
4
FUNCTIONAL EQUATIONS IN BANACH MODULES AND APPROXIMATE ALGEBRA HOMOMORPHISMS IN BANACH ALGEBRAS
Boo, DeokHoon ; Kenary, Hassan Azadi ; Park, Choonkil ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 33~52
DOI : 10.11568/kjm.2011.19.1.033
Abstract
We prove the HyersUlam stability of partitioned functional equations in Banach modules over a unital
algebra. It is applied to show the stability of algebra homomorphisms in Banach algebras associated with partitioned functional equations in Banach algebras.
5
CONVERGENCE OF INTEGRABLE SEMIGROUPS
Lee, Young S. ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 53~59
DOI : 10.11568/kjm.2011.19.1.053
Abstract
We study some properties of integrable semigroup and its generator, and then we establish convergence of integrable semigroups on the norming dual pairs.
6
A STUDY ON OPERATORS SATISFYING T
^{2}
 ≥ T
^{*}

^{2}
Lee, Jae Won ; Jeon, In Ho ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 61~64
DOI : 10.11568/kjm.2011.19.1.061
Abstract
Let
denotes the class of operators satisfying
. In this paper, we show if the restriction to a nontrivial invariant subspace
of an operator
is normal, then
reduces T.
7
AN APPLICATION OF THE LERAYSCHAUDER DEGREE THEORY TO THE VARIABLE COEFFICIENT SEMILINEAR BIHARMONIC PROBLEM
Choi, QHeung ; Jung, Tacksun ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 65~75
DOI : 10.11568/kjm.2011.19.1.065
Abstract
We obtain multiplicity results for the nonlinear biharmonic problem with variable coefficient. We prove by the LeraySchauder degree theory that the nonlinear biharmonic problem has multiple solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions.
8
QUADRATIC MAPPINGS ASSOCIATED WITH INNER PRODUCT SPACES
Lee, Sung Jin ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 77~85
DOI : 10.11568/kjm.2011.19.1.077
Abstract
In [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer
holds for all
,
,
. Let V, W be real vector spaces. It is shown that if an even mapping
satisfies
for all
,
,
, then the even mapping
is quadratic. Furthermore, we prove the generalized HyersUlam stability of the quadratic functional equation (0.1) in Banach spaces.
9
HOMOMORPHISMS IN PROPER LIE CQ
^{*}
ALGEBRAS
Lee, Jung Rye ; Shin, Dong Yun ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 87~99
DOI : 10.11568/kjm.2011.19.1.087
Abstract
Using the HyersUlamRassias stability method of functional equations, we investigate homomorphisms in proper
algebras and proper Lie
algebras, and derivations on proper
algebras and proper Lie
algebras associated with the following functional equation
for a fixed positive integer
.
10
TOPOLOGICAL APPROACH FOR THE MULTIPLE SOLUTIONS OF THE NONLINEAR PARABOLIC PROBLEM WITH VARIABLE COEFFICIENT JUMPING NONLINEARITY
Jung, Tacksun ; Choi, QHeung ;
Korean Journal of Mathematics, volume 19, issue 1, 2011, Pages 101~109
DOI : 10.11568/kjm.2011.19.1.101
Abstract
We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the LeraySchauder degree theory on the real Hilbert space.