DOI: 10.2298/fil2603975s ISSN: 0354-5180
Sequence spaces and operator ideals induced by the q-Bronze Leonardo-Lucas matrix
Shiva Shah, Bipan Hazarika
This paper introduces the q-Bronze Leonardo-Lucas matrix ℵ(q) =
(\tilde{\ell}_{nk}^{(q)})_{n,k\in\mathbb{N}}
, defined by
\tilde{\ell}_{nk}^{(q)}=\begin{cases} \dfrac{3q^{k-1}\tilde{\ell}_{k}(q)}{4\tilde{\ell}_{n}(q)+\tilde{\ell}_{n-1}(q)+3n-10}, & 1\le k\le n,\\ 0, & k>n, \end{cases}
with
\{\tilde{\ell}_{n}(q)\}
representing the
q
-Bronze Leonardo-Lucas sequence. Using
\tilde{\ell}_{n}(q)
is defined by
\tilde{\ell}_{n}(q)=(2+q^{n-1})\tilde{\ell}_{n-1}(q)+q^{n-1}\tilde{\ell}_{n-2}(q)-3
for
n\ge 2
,
\tilde{\ell}_{0}(q)=3
,
\tilde{\ell}_{1}(q)=4
. We introduce the matrix domains
\ell_{p}(\mathcal{N}(q))=(\ell_{p})_{\mathcal{N}(q)}
for
1\le p<\infty
, along with
\ell_{\infty}(\mathcal{N}(q))=(\ell_{\infty})_{\mathcal{N}(q)}
and
c(\mathcal{N}(q))=(c)_{\mathcal{N}(q)}
, which denotes the
q
-Bronze Leonardo-Lucas sequence spaces. In this context, we derive the Schauder basis for the space
\ell_{p}(\mathcal{N}(q))
for
1\le p<\infty
. We establish several results regarding the operator ideals associated with these newly defined sequence spaces. Further, we explore various geometric properties of
\ell_{p}(\mathcal{N}(q))
and
\ell_{\infty}(\mathcal{N}(q))
. Finally, we analyze the solidity property of these sequence spaces.