VOLUME 1, 2010 NUMBER 2
http://repository.enu.kz:8080/handle/123456789/1543
2020-03-31T00:34:10ZWEIGHTED HARDY INEQUALITIES AND THEIR APPLICATIONS TO OSCILLATION THEORY OF HALF–LINEAR DIFFERENTIAL EQUATIONS
http://repository.enu.kz:8080/handle/123456789/1564
WEIGHTED HARDY INEQUALITIES AND THEIR APPLICATIONS TO OSCILLATION THEORY OF HALF–LINEAR DIFFERENTIAL EQUATIONS
R. Oinarov; S.Y. Rakhimova; Communicated by A. Kufner
For the equation
(t)|y0(t)|p−2y0(t)
0
+ v(t)|y(t)|p−2y(t) = 0, t 2 (a, b)
where 1 < p < 1, we establish the properties of oscillation and nonoscillation.
2012-06-26T00:00:00ZSOME CHARACTERIZING CONDITIONS FOR THE HARDY INEQUALITY
http://repository.enu.kz:8080/handle/123456789/1563
SOME CHARACTERIZING CONDITIONS FOR THE HARDY INEQUALITY
A. Kufner; K. Kuliev
In this paper, a new scale of necessary and sufficient conditions for the
validity of the Hardy and reverse Hardy inequalities in the cases
0 < q
p < 1, p 2 (−1, 0) [ (1,1),
and
0 < p
q < 1, q 2 (0, 1)
is found and estimates for the best constants are derived.
2012-06-26T00:00:00ZON SUMMABILITY OF THE FOURIER COEFFICIENTS IN BOUNDED ORTHONORMAL SYSTEMS FOR FUNCTIONS FROM SOME LORENTZ TYPE SPACES
http://repository.enu.kz:8080/handle/123456789/1562
ON SUMMABILITY OF THE FOURIER COEFFICIENTS IN BOUNDED ORTHONORMAL SYSTEMS FOR FUNCTIONS FROM SOME LORENTZ TYPE SPACES
A.N. Kopezhanova; L.-E. Persson; Communicated by V. Guliyev
We denote by ( ), > 0, the Lorentz space equipped with the (quasi)
norm
kfk ( ) :=
Z 1
0
f (t)t
1
t
dt
t
!1
for a function f on [0,1] and with positive and equipped with some additional
growth properties. Some estimates of this quantity and some corresponding sums
of Fourier coefficients are proved for the case with a general orthonormal bounded
system.
2012-06-26T00:00:00ZON IMBALANCES IN ORIENTED BIPARTITE GRAPHS
http://repository.enu.kz:8080/handle/123456789/1561
ON IMBALANCES IN ORIENTED BIPARTITE GRAPHS
U. Samee; T.A. Chishti; Communicated by V.I. Burenkov
An oriented bipartite graph is the result of assigning a direction to each
edge of a simple bipartite graph. For any vertex x in an oriented bipartite graph
D(U, V ), let d+x and d−x respectively denote the outdegree and indegree of x. Define
aui = d+ui
− d−ui and bvj = d+vj
− d−vj respectively as the imbalances of vertices ui in U
and vj in V . In this paper, we obtain constructive and existence criteria for a pair of
sequences of integers to be the imbalances of some oriented bipartite graph. We also
show the existence of a bipartite oriented graph with given imbalance set.
2012-06-26T00:00:00Z