# Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

@article{Das2016SomePO, title={Some properties of Generalized Fibonacci difference bounded and \$p\$-absolutely convergent sequences}, author={Anupam Das and Bipan Hazarika}, journal={arXiv: Functional Analysis}, year={2016} }

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$
We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

## 7 Citations

On composition operators of Fibonacci matrix and applications of Hausdorff measure of noncompactness

- MathematicsBoletim da Sociedade Paranaense de Matemática
- 2022

The aim of the paper is introduced the composition of the two infinite matrices $\Lambda=(\lambda_{nk})$ and $\widehat{F}=\left( f_{nk} \right).$ Further, we determine the $\alpha$-, $\beta$-,…

Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces

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- 2018

Karakas and Karabudak [14], introduced the Lucas sequence spaces $X(E)$ and studied their some properties. The main purpose of this study is to introduce the Lucas difference sequence spaces…

Matrix transformation of Fibonacci band matrix on generalized $bv$-space and its dual spaces

- MathematicsBoletim da Sociedade Paranaense de Matemática
- 2018

In this paper we introduce a new sequence space $bv(\hat{F})$ by using the Fibonacci band matrix $\hat{F}.$ We also establish a few inclusion relations concerning this space and determine its…

On ideal convergence Fibonacci difference sequence spaces

- Mathematics
- 2018

The Fibonacci sequence was firstly used in the theory of sequence spaces by Kara and Başarir (Casp. J. Math. Sci. 1(1):43–47, 2012). Afterward, Kara (J. Inequal. Appl. 2013(1):38, 2013) defined the…

New structure of Fibonacci numbers using concept of Δ --operator

- MathematicsJournal of Mathematics and Computer Science
- 2021

The theory of sequence spaces is the fundamental of summability and applications to various sequences like Fibonacci sequences were deeply studied. In [A. H. Ganie, In: Matrix Theory-Applications and…

Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces

- MathematicsJournal of Inequalities and Applications
- 2019

Fibonacci difference matrix was defined by Kara in his paper (Kara in J. Inequal. Appl. 2013:38 2013). Recently, Khan et al. (Adv. Differ. Equ. 2018:199, 2018) using the Fibonacci difference matrix F…

Some new Fibonacci difference spaces of non-absolute type and compact operators

- Mathematics
- 2016

In this paper, we introduce the spaces and which are the BK-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the duals of those spaces and also construct…

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