Abstract
UDC 517.5
Let
p
=
(
p
j
)
and
q
=
(
q
k
)
be real sequences of nonnegative numbers with the property that
P
m
=
∑
j
=
0
m
p
j
≠
0
and
Q
n
=
∑
k
=
0
n
q
k
≠
0
for all
m
and
n
.
Let
(
P
m
)
and
(
Q
n
)
be regulary varying positive indices. Assume that
(
u
m
n
)
is a double sequence of complex (real) numbers, which is
(
N
¯
,
p
,
q
;
α
,
β
)
summable with a finite limit, where
(
α
,
β
)
=
(
1,1
)
,
(
1,0
)
, or
(
0,1
)
. We present some conditions imposed on the weights under which
(
u
m
n
)
converges in Pringsheim's sense. These results generalize and extend the results obtained by authors in [Comput. Math. Appl., <strong>62</strong>, No. 6, 2609–2615 (2011)].
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
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