Power series methods and statistical limit superior
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
Abstract
Given a real bounded sequence
x
=
(
x
j
)
and an infinite matrix
A
=
(
a
n
j
)
Knopp core theorem is equivalent to study the inequality
l
i
m
s
u
p
A
x
≤
l
i
m
s
u
p
x
.
Recently Fridy and Orhan [6] have considered some variants of this inequality by replacing
l
i
m
s
u
p
x
with statistical limit superior
s
t
−
l
i
m
s
u
p
x
. In the present paper we examine similar type of inequalities by employing a power series method
P
; a non-matrix sequence-to-function transformation, in place of
A
=
(
a
n
j
)
.
Description
Keywords
Natural density, statistical convergence, statistical limit superior, core of a sequence, power series methods