Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On Motzkin sequence spaces via q -analog and compact operators
View through CrossRef
Abstract
We aim to develop a
q
q
-analog of recently introduced Motzkin sequence spaces by Erdem et al. [
Motzkin sequence spaces and Motzkin core
, Numer. Funct. Anal. Optim.
45
(2024), no. 4–6, 283–303] by using
q
q
-Motzkin numbers and introduce sequence spaces
c
(
M
(
q
)
)
c\left({\mathfrak{M}}\left(q))
and
c
0
(
M
(
q
)
)
.
{c}_{0}\left({\mathfrak{M}}\left(q)).
We investigate some topological properties, compute bases, and obtain their duals. For
X
∈
{
c
(
M
(
q
)
)
,
c
0
(
M
(
q
)
)
}
X\in \{c\left({\mathfrak{M}}\left(q)),{c}_{0}\left({\mathfrak{M}}\left(q))\}
and
Y
∈
{
ℓ
∞
,
c
,
c
0
,
ℓ
1
}
,
Y\in \{{\ell }_{\infty },c,{c}_{0},{\ell }_{1}\},
some results pertaining to characterization of matrix class
(
X
,
Y
)
\left(X,Y)
is given. We devote the final section to obtain necessary and sufficient conditions for a matrix operator to be compact on the space
c
0
(
M
(
q
)
)
{c}_{0}\left({\mathfrak{M}}\left(q))
via Hausdorff measure of noncompactness.
Title: On Motzkin sequence spaces via
q
-analog and compact operators
Description:
Abstract
We aim to develop a
q
q
-analog of recently introduced Motzkin sequence spaces by Erdem et al.
[
Motzkin sequence spaces and Motzkin core
, Numer.
Funct.
Anal.
Optim.
45
(2024), no.
4–6, 283–303] by using
q
q
-Motzkin numbers and introduce sequence spaces
c
(
M
(
q
)
)
c\left({\mathfrak{M}}\left(q))
and
c
0
(
M
(
q
)
)
.
{c}_{0}\left({\mathfrak{M}}\left(q)).
We investigate some topological properties, compute bases, and obtain their duals.
For
X
∈
{
c
(
M
(
q
)
)
,
c
0
(
M
(
q
)
)
}
X\in \{c\left({\mathfrak{M}}\left(q)),{c}_{0}\left({\mathfrak{M}}\left(q))\}
and
Y
∈
{
ℓ
∞
,
c
,
c
0
,
ℓ
1
}
,
Y\in \{{\ell }_{\infty },c,{c}_{0},{\ell }_{1}\},
some results pertaining to characterization of matrix class
(
X
,
Y
)
\left(X,Y)
is given.
We devote the final section to obtain necessary and sufficient conditions for a matrix operator to be compact on the space
c
0
(
M
(
q
)
)
{c}_{0}\left({\mathfrak{M}}\left(q))
via Hausdorff measure of noncompactness.
Related Results
Motzkin Paths, Motzkin Polynomials and Recurrence Relations
Motzkin Paths, Motzkin Polynomials and Recurrence Relations
We consider the Motzkin paths which are simple combinatorial objects appearing in many contexts. They are counted by the Motzkin numbers, related to the well known Catalan numbers....
A Touch of Space Weather - Outreach project for visually impaired students
A Touch of Space Weather - Outreach project for visually impaired students
<p><em><span data-preserver-spaces="true">'A Touch of Space Weather' is a project that brings space weather science into...
Enhancing analog circuit security through obfuscation
Enhancing analog circuit security through obfuscation
The focus of this dissertation is the safeguarding of analog circuits against IP piracy attacks, which includes the development of a novel method to secure analog IP, the assessmen...
Theia can arrive late and be oxidized, but not if it is large compared to proto-Earth
Theia can arrive late and be oxidized, but not if it is large compared to proto-Earth
The Moon-forming impact was the most significant event during the accretion of Earth substantially establishing the physical and chemical states of the Earth-Moon system. In the ca...
Functional Analysis
Functional Analysis
Abstract
The article contains sections titled:
Banach Space and Operators on Them
Vector and Normed Spaces
...
COST – EFFECTIVENESS ANALYSIS OF USING ANTIDIABETIC IN OUTPATIENT WITH TYPE 2 DIABETES MELLITUS
COST – EFFECTIVENESS ANALYSIS OF USING ANTIDIABETIC IN OUTPATIENT WITH TYPE 2 DIABETES MELLITUS
Type 2 diabetes Mellitus is a chronic disease that requires lifelong treatment. In the course of the disease, if blood sugar levels are not controlled, it can lead to complications...
Analog Convolutional Operator Circuit for Low-Power Mixed-Signal CNN Processing Chip
Analog Convolutional Operator Circuit for Low-Power Mixed-Signal CNN Processing Chip
In this paper, we propose a compact and low-power mixed-signal approach to implementing convolutional operators that are often responsible for most of the chip area and power consu...
When Circuits Grow Food: The Ever-Present Analog Electronics Driving Modern Agriculture
When Circuits Grow Food: The Ever-Present Analog Electronics Driving Modern Agriculture
Analog electronics, i.e., circuits that process continuously varying signals, have quietly powered the backbone of agricultural automation long before the modern wave of digital te...