q-Fibonacci sequence spaces and related matrix transformations
In this paper, we define the sequence spaces ℓ p ( F ^ q ) 1 ≤ p < ∞ , ℓ ∞ ( F ^ q ) , c 0 ( F ^ q ) and c ( F ^ q ) by using q -Fibonacci band matrix F ^ q defined by F ^ q = F ^ nk ( q ) = - F n + 1 ( q ) - 1 q n F n ( q ) , k = n - 1 F n + 2 ( q ) - 1 q n F n ( q ) , k = n 0 , otherwise ( k ,...
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| Published in: | Journal of applied mathematics & computing Vol. 69; no. 2; pp. 2135 - 2154 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01-04-2023
Springer Nature B.V |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | In this paper, we define the sequence spaces
ℓ
p
(
F
^
q
)
1
≤
p
<
∞
,
ℓ
∞
(
F
^
q
)
,
c
0
(
F
^
q
)
and
c
(
F
^
q
)
by using
q
-Fibonacci band matrix
F
^
q
defined by
F
^
q
=
F
^
nk
(
q
)
=
-
F
n
+
1
(
q
)
-
1
q
n
F
n
(
q
)
,
k
=
n
-
1
F
n
+
2
(
q
)
-
1
q
n
F
n
(
q
)
,
k
=
n
0
,
otherwise
(
k
,
n
∈
N
)
.
We study some topological properties and give some inclusion relations for these spaces. In addition, we build a bases for the space
ℓ
p
(
F
^
q
)
, compute
α
-,
β
-,
γ
- duals of the same space, characterize some matrix classes and examine some geometric properties. |
|---|---|
| ISSN: | 1598-5865 1865-2085 |
| DOI: | 10.1007/s12190-022-01825-9 |