Affiliation:
1. Department of Mathematics , School of Basic Sciences , 30071 CSJM University , Kanpur - 208024 , India
Abstract
Abstract
The primary objective of this paper is to create a novel infinite Toeplitz matrix by leveraging Tetranacci numbers. This matrix serves as the foundation for defining new sequence spaces denoted as
c
0
(
G
)
{c_{0}(G)}
,
c
(
G
)
{c(G)}
,
ℓ
∞
(
G
)
{\ell_{\infty}(G)}
, and
ℓ
p
(
G
)
{\ell_{p}(G)}
, where
1
≤
p
<
∞
{1\leq p<\infty}
. By utilizing this newly constructed matrix, the paper also explores and examines various algebraic and topological properties inherent to the sequence spaces
c
0
(
G
)
{c_{0}(G)}
,
c
(
G
)
{c(G)}
,
ℓ
∞
(
G
)
{\ell_{\infty}(G)}
, and
ℓ
p
(
G
)
{\ell_{p}(G)}
for values of p within the range of
1
≤
p
<
∞
{1\leq p<\infty}
. At last, we also prove existence theorem with example for infinite systems of differential equations in
ℓ
p
(
G
)
{\ell_{p}(G)}
.