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

Das, Anupam; Hazarika, Bipan

doi:10.5269/bspm.v36i3.32010

Cited by 9 publications

(7 citation statements)

References 13 publications

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“…Since then many authors studied and generalized Fibonacci difference sequence spaces. We refer to [11,13,14,16,[30][31][32][33][34] for relevant studies. Motivated by the above studies, we introduced generalized Fibonacci difference operator by the composition of the Fibonacci band matrix F and the triple band matrix B(x, y, z).…”

Section: Fibonacci Sequence Spacesmentioning

confidence: 99%

Sequence spaces derived by the triple band generalized Fibonacci difference operator

Yaying¹,

Hazarika

Mohiuddine

et al. 2020

Adv Differ Equ

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In this article we introduce the generalized Fibonacci difference operator $\mathsf{F}(\mathsf{B})$ F ( B ) by the composition of a Fibonacci band matrix and a triple band matrix $\mathsf{B}(x,y,z)$ B ( x , y , z ) and study the spaces $\ell _{k}( \mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) . We exhibit certain topological properties, construct a Schauder basis and determine the Köthe–Toeplitz duals of the new spaces. Furthermore, we characterize certain classes of matrix mappings from the spaces $\ell _{k}(\mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) to space $\mathsf{Y}\in \{\ell _{\infty },c_{0},c,\ell _{1},cs_{0},cs,bs\}$ Y ∈ { ℓ ∞ , c 0 , c , ℓ 1 , c s 0 , c s , b s } and obtain the necessary and sufficient condition for a matrix operator to be compact from the spaces $\ell _{k}(\mathsf{F}(\mathsf{B}))$ ℓ k ( F ( B ) ) and $\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ ℓ ∞ ( F ( B ) ) to $\mathsf{Y}\in \{ \ell _{\infty }, c, c_{0}, \ell _{1},cs_{0},cs,bs\} $ Y ∈ { ℓ ∞ , c , c 0 , ℓ 1 , c s 0 , c s , b s } using the Hausdorff measure of non-compactness.

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Section: Fibonacci Sequence Spacesmentioning

confidence: 99%

Sequence spaces derived by the triple band generalized Fibonacci difference operator

Yaying¹,

Hazarika

Mohiuddine

et al. 2020

Adv Differ Equ

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“…It is easy to see that X A is a sequence space whenever X is a sequence space. In the past, several authors studied matrix transformations on sequence spaces that are the matrix domain of the difference operator, or of the matrices of some classical methods of summability in different sequence spaces, for instance we refer to [7,8,9,19,20,21,22,25,28,36,37,38] and references therein. The Hausdorff measure of non-compactness of linear operators given by infinite matrices in some special classes of sequence spaces were studied in [1,6,27,29,32].…”

Section: Introductionmentioning

confidence: 99%

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

Hazarika

Das

Kara

et al. 2022

bspm

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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 $\alpha$-, $\beta$-, $\gamma$-duals of new spaces and also construct the basis for the space $\ell_{p}^{\lambda}(\widehat{F}).$ Additionally, we characterize some matrix classes on the spaces $\ell_{\infty}^{\lambda}(\widehat{F})$ and $\ell_{p}^{\lambda}(\widehat{F}).$ We also investigate some geometric properties concerning Banach-Saks type $p.$Finally we characterize the subclasses $\mathcal{K}(X:Y)$ of compact operators by applying the Hausdorff measure of noncompactness, where $X\in\{\ell_{\infty}^{\lambda}(\widehat{F}),\ell_{p}^{\lambda}(\widehat{F})\}$ and $Y\in\{c_{0},c, \ell_{\infty}, \ell_{1}, bv\},$ and $1\leq p<\infty.$

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“…for all r, k ∈ N, and as in [2,6,14,27,44], {f r } ∞ r=0 represents the sequence of Fibonacci numbers defined by the linear recurrence equalities f 0 = f 1 = 1 and f r = f r−1 + f r−2 , r 2, with the following fundamental properties:…”

Section: Introductionmentioning

confidence: 99%

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

Fathima¹,

AlBaidani²,

Ganie³

et al. 2021

J. Math. Computer Sci.

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

Abstract: In this paper we introduce a new sequence space bv(F ) by using the Fibonacci band matrixF . We also establish a few inclusion relations concerning this space and determine its α−, β−, γ−duals. Finally we characterize some matrix classes on the space bv(F ).

Cited by 9 publications

References 13 publications

Sequence spaces derived by the triple band generalized Fibonacci difference operator

Sequence spaces derived by the triple band generalized Fibonacci difference operator

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

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

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