基于带矩阵的q-Fibonacci Cesàro序列空间

IF 1.4 4区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES
Ravi Kumar, Sunil K. Sharma, Ajay K. Sharma, M. Musarleen
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引用次数: 0

摘要

本文利用$$\begin{aligned}\tilde{\mathcal {G}}_q=\tilde{\mathcal {G}}_{rk}(q)= \left\{ \begin{array}{ll} -\frac{\mathcal {G}_{r+1}(q)-1}{q^r \mathcal {G}_r(q)},&{}\quad k=r-1\\ \frac{\mathcal {G}_{r+2}(q)-1}{q^r \mathcal {G}_r(q)},&{}\quad k=r\\ 0,&{}\quad \text {otherwise}, \end{array}\right. \end{aligned}$$\(\text {where}~ (k,r \in \mathbb {N}).\)定义的q-Fibonacci带矩阵\(\tilde{\mathcal {G}}_q\)定义了新的序列空间\(Ces_p(\tilde{\mathcal {G}}_q)~ (1\le p<\infty )\)和\(Ces_\infty (\tilde{\mathcal {G}}_q)\),并研究了这些空间的一些拓扑性质和包含关系。我们还建立了空间\(Ces_p(\tilde{\mathcal {G}}_q)\)的基,计算了同一空间的\(\alpha\) -对偶,刻画了一些矩阵类,研究了一些几何性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On q-Fibonacci Cesàro Sequence Spaces by Using Band Matrix

In this paper, we define the new sequence spaces \(Ces_p(\tilde{\mathcal {G}}_q)~ (1\le p<\infty )\) 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.

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来源期刊
CiteScore
4.00
自引率
5.90%
发文量
122
审稿时长
>12 weeks
期刊介绍: The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences
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