On q-Fibonacci Cesàro Sequence Spaces by Using Band Matrix

Abstract

In this paper, we define the new sequence spaces \(Ces_p(\tilde{\mathcal {G}}_q)~ (1\le p<\infty )\) and \(Ces_\infty (\tilde{\mathcal {G}}_q)\) by using q-Fibonacci band matrix \(\tilde{\mathcal {G}}_q\) defined by

$$\begin{aligned}\tilde{\mathcal {G}}_q=\tilde{\mathcal {G}}_{rk}(q)= \left\{ \begin{array}{ll} -\frac{\mathcal {G}_{r+1}(q)-1}{q^r \mathcal {G}_r(q)},&{}\quad k=r-1\\ \frac{\mathcal {G}_{r+2}(q)-1}{q^r \mathcal {G}_r(q)},&{}\quad k=r\\ 0,&{}\quad \text {otherwise}, \end{array}\right. \end{aligned}$$

\(\text {where}~ (k,r \in \mathbb {N}).\) We examine some topological properties and some inclusion relation for these spaces. We also make an effort to build a basis for the space \(Ces_p(\tilde{\mathcal {G}}_q)\), compute \(\alpha\)-duals of the same space, characterize some matrix classes and study some geometric properties.