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

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Anupam Das, Bipan Hazarika

Functional Analysis · Submitted 1 Apr 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID1604.00182 (version 1)
Pith ID6YSHBX6F, Pith's permanent record of this paper and its review
CitationAnupam Das, Bipan Hazarika. "Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences." arXiv:1604.00182 (2016). https://pith.science/paper/6YSHBX6F
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,427 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.04 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.09 · mentions code or data availability 0.02.

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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.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 1.00 0.95 0.44 asserted 1.00
s1 We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space. contribution 0.98 0.94 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

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.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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  • The matrix domain $X_A$ of an infinite matrix $A$ in a sequence space $X$ is defined by [equation] Kizmaz [ref] introduecd the notion of the difference operator $Δ.$ The operator $Δ$ denote the matrix $Δ=(Δ_nk)$ defined by [equation] In the past, several authors studied matirx transformation 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 [ref] and references therein.

    Some new Fibonacci difference spaces of non-absolute type and compact operators · Introduction · 0.98

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