On q-Fibonacci Cesàro Sequence Spaces by Using Band Matrix

In this paper, we define the new sequence spaces \(Ces_p(\tilde{\mathcal {G}}_q)~ (1\le p<\infty )\) $Ce{s}_p({\tilde{\mathcal{G}}}_q)(1\le p<\infty )$ and \(Ces_\infty (\tilde{\mathcal {G}}_q)\) $Ce{s}_{\infty }({\tilde{\mathcal{G}}}_q)$ by using q-Fibonacci band matrix \(\tilde{\mathcal {G}}_q\) ${\tilde{\mathcal{G}}}_q$ defined by \(\begin{aligned}\tilde{\mathcal {G}}_q=\tilde{\mathcal {G}}_{rk}(q)= \left\{ \begin{array}{ll} -\frac{\mathcal {G}_{r+1}(q)-1}{q^r \mathcal {G}_r(q)},&{}\quad k=r-1\\ \frac{\mathcal {G}_{r+2}(q)-1}{q^r \mathcal {G}_r(q)},&{}\quad k=r\\ 0,&{}\quad \text {otherwise}, \end{array}\right. \end{aligned}\) $$\begin{array}{c}\hfill {\tilde{\mathcal{G}}}_q={\tilde{\mathcal{G}}}_{\mathit{rk}}(q)=\left\{\begin{array}{cc}-\frac{{\mathcal{G}}_{r+1}(q)-1}{q^r{\mathcal{G}}_r(q)},\hfill & k=r-1\hfill \\ \frac{{\mathcal{G}}_{r+2}(q)-1}{q^r{\mathcal{G}}_r(q)},\hfill & k=r\hfill \\ 0,\hfill & \text{otherwise},\hfill \end{array}\right)\end{array}$$ \(\text {where}~ (k,r \in \mathbb {N}).\) $\text{where}(k,r\in \mathbb{N}).$ We examine some topological properties and some inclusion relation for these spaces. We also make an effort to build a basis for the space \(Ces_p(\tilde{\mathcal {G}}_q)\) $Ce{s}_p({\tilde{\mathcal{G}}}_q)$ , compute \(\alpha\) $\alpha$ -duals of the same space, characterize some matrix classes and study some geometric properties.