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Kyungpook mathematical journal
Journal Basic Information
pISSN :
1225-6951
eISSN :
0454-8124
Journal DOI :
10.5666/KMJ
Frequency :
Others
Publisher:
Department of Mathematics, Kyungpook National University
Editor in Chief :
Sang-Dong Kim
Volume & Issues
Volume 49, Issue 4 - Dec 2009
Volume 49, Issue 3 - Sep 2009
Volume 49, Issue 2 - Jun 2009
Volume 49, Issue 1 - Mar 2009
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1
Riccati Equation and Positivity of Operator Matrices
Fujii, Jun Ichi ; Fujii, Masatoshi ; Nakamoto, Ritsuo ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 595~603
DOI : 10.5666/KMJ.2009.49.4.595
Abstract
We show that for an algebraic Riccati equation
, its solutions are given by X = W + BT for some solution W of
=
. To generalize this, we give an equivalent condition for
for given positive operators B and A, by which it can be regarded as Riccati inequality
. As an application, the harmonic mean B ! C is explicitly written even if B and C are noninvertible.
2
A Stage-Structured Predator-Prey System with Time Delay and Beddington-DeAngelis Functional Response
Wang, Lingshu ; Xu, Rui ; Feng, Guanghui ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 605~618
DOI : 10.5666/KMJ.2009.49.4.605
Abstract
A stage-structured predator-prey system with time delay and Beddington-DeAngelis functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.
3
Scaling Law of the Hausdorff Measure
Baek, Hun-Ki ; Lee, Hung-Hwan ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 619~621
DOI : 10.5666/KMJ.2009.49.4.619
Abstract
We exhibit an example that the scaling property of Hausdorff measure on
does not hold.
4
On the Hilbert Type Integral Inequalities with Some Parameters and Its Reverse
Yildirim, Huseyin ; Ozkan, Umut Mutlu ; Sarikaya, Mehmet Zeki ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 623~630
DOI : 10.5666/KMJ.2009.49.4.623
Abstract
This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.
5
On a Class of Meromorphic Functions Defined by Certain Linear Operators
Kumar, Shanmugam Sivaprasad ; Taneja, Harish Chander ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 631~646
DOI : 10.5666/KMJ.2009.49.4.631
Abstract
In the present investigation, we introduce new classes of p-valent meromorphic functions defined by Liu-Srivastava linear operator and the multiplier transform and study their properties by using certain first order differential subordination and superordination.
6
On the Iterated Duggal Transforms
Cho, Muneo ; Jung, Il-Bong ; Lee, Woo-Young ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 647~650
DOI : 10.5666/KMJ.2009.49.4.647
Abstract
For a bounded operator T =
(polar decomposition), we consider a transform b
=
and discuss the convergence of iterated transform of
under the strong operator topology. We prove that such iteration of quasiaffine hyponormal operator converges to a normal operator under the strong operator topology.
7
Uniqueness of Meromorphic Functions Sharing a Small Function with Their Differential Polynomials
Banerjee, Abhijit ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 651~666
DOI : 10.5666/KMJ.2009.49.4.651
Abstract
With the aid of weakly weighted sharing and a recently introduced sharing notion in [3] known as relaxed weighted sharing we investigate the uniqueness of meromorphic functions sharing a small function with its differential polynomials. Our results will improve and supplement all the results obtained by Zhang and Yang [17] as well as a substantial part of the results recently obtained by the present author [2] and thus provide a better answer to the questions posed by Yu [14] in this regard.
8
Approximating Common Fixed Points of One-step Iterative Scheme with Error for Asymptotically Quasi-nonexpansive Type Nonself-Mappings
Puturong, Narongrit ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 667~674
DOI : 10.5666/KMJ.2009.49.4.667
Abstract
In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically non-expansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.
9
Uniqueness and Value-sharing of Entire Functions
Li, Xiaojuan ; Meng, Chao ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 675~682
DOI : 10.5666/KMJ.2009.49.4.675
Abstract
In this paper, we study the uniqueness problems on entire functions sharing one value. We improve and generalize some previous results of Zhang and Lin [11]. On the one hand, we consider the case for some more general differential polynomials
where
is a polynomial; on the other hand, we relax the nature of sharing value from CM to IM.
10
Weakly Hyponormal Composition Operators and Embry Condition
Lee, Mi-Ryeong ; Park, Jung-Woi ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 683~689
DOI : 10.5666/KMJ.2009.49.4.683
Abstract
We investigate the gaps among classes of weakly hyponormal composition operators induced by Embry characterization for the subnormality. The relationship between subnormality and weak hyponormality will be discussed in a version of composition operator induced by a non-singular measurable transformation.
11
A Fixed Point Approach to the Stability of Quadratic Equations in Quasi Normed Spaces
Mirmostafaee, Alireza Kamel ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 691~700
DOI : 10.5666/KMJ.2009.49.4.691
Abstract
We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.
12
Approximation of Common Fixed Points for a Family of Non-Lipschitzian Mappings
Kim, Tae-Hwa ; Park, Yong-Kil ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 701~712
DOI : 10.5666/KMJ.2009.49.4.701
Abstract
In this paper, we first introduce a family S = {
: C
C} of non-Lipschitzian mappings, called total asymptotically nonexpansive (briefly, TAN) on a nonempty closed convex subset C of a real Banach space X, and next give necessary and sufficient conditions for strong convergence of the sequence {
} defined recursively by the algorithm
=
,
, starting from an initial guess
, to a common fixed point for such a continuous TAN family S in Banach spaces. Finally, some applications to a finite family of TAN self mappings are also added.
13
Convolution Properties of Certain Class of Multivalent Meromorphic Functions
Vijaywargiya, Pramila ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 713~723
DOI : 10.5666/KMJ.2009.49.4.713
Abstract
The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory.
14
Embedding in a Direct Limit
Rubin, Leonard Roy ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 725~729
DOI : 10.5666/KMJ.2009.49.4.725
Abstract
Let X be a direct system of topological spaces and X its direct limit. We show that under certain conditions the direct limit of a "subsystem" of X embeds in a canonical way as a closed subspace of X.
15
On a Reverse of the Slightly Sharper Hilbert-type Inequality
Zhong, Jianhua ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 731~742
DOI : 10.5666/KMJ.2009.49.4.731
Abstract
In this paper, by introducing parameters
,
and two pairs of conjugate exponents (p, q), (r, s) and applying the improved Euler-Maclaurin's summation formula, we establish a reverse of the slightly sharper Hilbert-type inequality. As applications, the strengthened version and the equivalent form are given.
16
An Application of Furuta Inequality to Linear Operator Equations
Ahn, Eun-Kyung ; Lim, Yong-Do ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 743~750
DOI : 10.5666/KMJ.2009.49.4.743
Abstract
A class of Hermitian operators B admitting a positive semidefinite solution of the linear operator equation
for a fixed positive definite operator A is given via the Furuta inequality.
17
Some Properties of Harmonic Functions Defined by Convolution
Dixit, Kaushal Kishor ; Porwal, Saurabh ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 751~761
DOI : 10.5666/KMJ.2009.49.4.751
Abstract
In this paper, we introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by Frasin [3] and obtain coefficient bounds, distortion bounds and extreme points, convolution conditions and convex combination are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to those corresponding previously known results.
18
Extinction and Permanence of a Holling I Type Impulsive Predator-prey Model
Baek, Hun-Ki ; Jung, Chang-Do ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 763~770
DOI : 10.5666/KMJ.2009.49.4.763
Abstract
We investigate the dynamical properties of a Holling type I predator-prey model, which harvests both prey and predator and stock predator impulsively. By using the Floquet theory and small amplitude perturbation method we prove that there exists a stable prey-extermination solution when the impulsive period is less than some critical value, which implies that the model could be extinct under some conditions. Moreover, we give a sufficient condition for the permanence of the model.
19
Some Further Results on Entire Functions That Share Fixed-Points
Qi, Xiao-Guang ; Dou, Jia ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 771~777
DOI : 10.5666/KMJ.2009.49.4.771
Abstract
In this paper, we study the uniqueness problem on entire functions sharing fixed points and prove some theorems which are related to one famous problem of Hayman.
20
On Generalized ø-Recurrent LP-Sasakian Manifolds
Jaiswal, Jai Prakash ; Ojha, Ram Hit ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 779~788
DOI : 10.5666/KMJ.2009.49.4.779
Abstract
In this paper we studied generalized
-recurrent and generalized concircular
-recurrent LP-Sasakian manifolds.
21
A Class of Lorentzian α-Sasakian Manifolds
Yildiz, Ahmet ; Turan, Mine ; Murathan, Cengizhan ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 789~799
DOI : 10.5666/KMJ.2009.49.4.789
Abstract
In this study we consider
-conformally flat,
-conharmonically flat,
-projectively at and
-concircularly flat Lorentzian
-Sasakian manifolds. In all cases, we get the manifold will be an
-Einstein manifold.
22
Knots with a Trivial Coefficient Polynomial
Miyazawa, Yasuyuki ;
Kyungpook mathematical journal, volume 49, issue 4, 2009, Pages 801~809
DOI : 10.5666/KMJ.2009.49.4.801
Abstract
By using a tangle decomposition of a knot, we give a method for the construction of a knot with the lowest trivial HOMFLY coefficient polynomial. Applying this, we show that there exist infinitely many 2-bridge knots with such a coefficient polynomial.