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The Pure and Applied Mathematics
Journal Basic Information
pISSN :
1226-0657
eISSN :
2287-6081
Journal DOI :
10.7468/jksmeb
Frequency :
Others
Publisher:
Korea Society of Mathematical Education
Editor in Chief :
Volume & Issues
Volume 15, Issue 4 - Nov 2008
Volume 15, Issue 3 - Aug 2008
Volume 15, Issue 2 - May 2008
Volume 15, Issue 1 - Feb 2008
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1
FINITE EXTENSIONS OF WEIGHTED WORD L-DELTA GROUPS
Ryang, Do-Hyoung ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 353~364
Abstract
The purpose of this paper is to investigate the finite extension of weighted word L-delta groups. The paper revealed that a finite extension of a weighted word L-delta group is a weighted word L-delta group, and an abelian group, in addition, is a weighted word L-delta group and simultaneously a word L-delta group.
2
A COMPARATIVE STUDY BETWEEN CONVERGENCE RESULTS FOR NEWTON'S METHOD
Argyros, Ioannis K. ; Hilout, Said ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 365~375
Abstract
We present a new theorem for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Under a gamma-type condition we show that we can extend the applicability of Newton's method given in [12]. We also provide a comparative study between results using the classical Newton-Kantorovich conditions ([6], [7], [10]), and the ones using the gamma-type conditions ([12], [13]). Numerical examples are also provided.
3
FUZZY ABYSMS OF HILBERT ALGEBRAS
Jun, Young-Bae ; Lee, Kyoung-Ja ; Park, Chul-Hwan ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 377~385
Abstract
The notion of fuzzy abysms in Hilbert algebras is introduced, and several properties are investigated. Relations between fuzzy subalgebra, fuzzy deductive systems, and fuzzy abysms are considered.
4
MONOTONICITY AND LOGARITHMIC CONVEXITY OF THREE FUNCTIONS INVOLVING EXPONENTIAL FUNCTION
Guo, Bai-Ni ; Liu, Ai-Qi ; Qi, Feng ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 387~392
Abstract
In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions
are decreasing in (0,
) and the function
for a
is logarithmically concave.
5
ON AN ADDITIVE FUNCTIONAL INEQUALITY IN NORMED MODULES OVER A
-ALGEBRA
An, Jong-Su ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 393~400
Abstract
In this paper, we investigate the following additive functional inequality (0.1) ||f(x)+f(y)+f(z)+f(w)||
||f(x+y)+f(z+w)|| in normed modules over a
-algebra. This is applied to understand homomor-phisms in
-algebra. Moreover, we prove the generalized Hyers-Ulam stability of the functional inequality (0.2) ||f(x)+f(y)+f(z)f(w)||
||f(x+y+z+w)||+
in real Banach spaces, where
, p are positive real numbers with
.
6
HILBERT-SCHMIDT INTERPOLATION ON AX=Y IN A TRIDIAGONAL ALGEBRA ALG
Kang, Joo-Ho ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 401~406
Abstract
Given operators X and Y acting on a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that AX=Y. In this article, we investigate Hilbert-Schmidt interpolation problems for operators in a tridiagonal algebra and we get the following: Let
be a subspace lattice acting on a separable complex Hilbert space H and let X=
and Y=
be operators acting on H. Then the following are equivalent: (1) There exists a Hilbert-Schmidt operator
in Alg
such that AX=Y. (2) There is a bounded sequence
in
such that
<
and
.
7
POSITIVE SOLUTIONS OF SELF-ADJOINT BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE
Yang, Aijun ; Ge, Weigao ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 407~414
Abstract
In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x'(t))'+f(t,x(t))=0, t
(0,1), x'(0)=0, x(1) =
x(s)g(s)ds. A new result on the existence of positive solutions is obtained. The interesting points are: the first, we employ a new tool-the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.
8
AN IMPROVEMENT OF THE MADDOX THEOREM ON THE MATRIX CLASS
Yoo, Won-Sok ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 415~421
Abstract
A clear-cut characterization of the matrix class
is obtained for a very general case.
9
MINTY'S LEMMA FOR STRONG IMPLICIT VECTOR VARIATIONAL INEQUALITY SYSTEMS
Kim, Seung-Hyun ; Lee, Byung-Soo ;
The Pure and Applied Mathematics, volume 15, issue 4, 2008, Pages 423~432
Abstract
In this paper, we consider a new Minty's Lemma for strong implicit vector variational inequality systems and obtain some existence results for systems of strong implicit vector variational inequalities which generalize some results in [1].