A Note on the Sequence Space b_p^(r,s) (G)

Bişgin, Mustafa Cemil

doi:10.17776/csj.363211

Cited by 3 publications

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References 10 publications

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“…Afterwards, Altay and Polat [10] improved works in [7][8][9] by defining the sequence spaces 𝑒 0 𝑟 (∆), 𝑒 𝑐 𝑟 (∆) and 𝑒 ∞ 𝑟 (∆) in [10] as: Recently, Bişgin [14,15] has further generalized works in [7][8][9] Subsequently, when the Binomial matrix and generalized difference matrix 𝐺 = (𝑔 𝑛𝑘 ) is considered, the sequence space 𝑏 𝑝 𝑟,𝑠 (𝐺) has been defined by Bişgin in [16] as follows:…”

Section: The Sequence Space 𝒃 𝒑 𝒓𝒔 (𝑫)mentioning

confidence: 99%

Some Notes on the New Sequence Space b_p^(r,s) (D)

Sönmez

2020

Gazi University Journal of Science

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Highlights• The 𝑏 𝑝 𝑟,𝑠 (𝐷) is defined by means of the composition of the Binomial matrix and triple band matrix.• The space 𝑏 𝑝 𝑟,𝑠 (𝐷) is linearly isomorphic to the space 𝑙 𝑝 . where 1 ≤ 𝑝 < ∞.• Some inclusion relations and Schauder basis of the space 𝑏 𝑝 𝑟,𝑠 (𝐷) are obtained.• 𝛼-, 𝛽and 𝛾-duals of the space 𝑏 𝑝 𝑟,𝑠 (𝐷) are calculated .

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Section: The Sequence Space 𝒃 𝒑 𝒓𝒔 (𝑫)mentioning

confidence: 99%

Some Notes on the New Sequence Space b_p^(r,s) (D)

Sönmez

2020

Gazi University Journal of Science

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New Integrated and Differentiated Sequence Spaces ∫ b_p^(r,s) and db_p^(r,s)

Topal

2024

SAUJS

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In this work, we construct new sequence spaces by combining the integrated and differentiated sequence spaces with the binomial matrix. Firstly, we provide information about basic matters such as sequence spaces and matrix domain. Subsequently we briefly summarize some sequence spaces generated by the binomial matrix. Thereafter, we define the integrated and differentiated sequence spaces and establish the new sequence spaces. Afterwards, we examine some properties and the inclusion relations of these new sequence spaces. We also determine the α, β and γ-duals of the integrated and differentiated sequence spaces. Finally, we characterize some matrix classes associated with the new sequence spaces.

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New Sequence Spaces Derived by the Composition of Binomial and Quadruple Band Matrices

Topal

2024

Recep Tayyip Erdoğan Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi

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In this work, we construct the sequence spaces b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q), derived from the combination of binomial and quadruple band matrices, where Q is a quadruple band matrix. The study is divided into four main sections. The first section provides some fundamental definitions and equations that will be used later. In the second section, detailed discussions are made on some works previously completed by various authors using the domain of the binomial matrix. Then, the three new sequence spaces b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) are defined. It is then shown that these obtained sequence spaces are BK-spaces. Following this, it is demonstrated that b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) sequence spaces are linearly isomorphic to the spaces c_0, c and l_∞, in turn, followed by some inclusion relations. In the third section, the Schauder bases of the new sequence spaces b_0^(a,b) (Q) and b_c^(a,b) (Q) are provided, and the α-, β- and γ- duals of b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) sequence spaces are determined. The fourth section characterizes some matrix classes. As a result, it is observed that the new matrix obtained from the combination of binomial and quadruple band matrices provides more general and comprehensive results than those obtained previously.

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A Note on the Sequence Space b_p^(r,s) (G)

Cited by 3 publications

References 10 publications

Some Notes on the New Sequence Space b_p^(r,s) (D)

Some Notes on the New Sequence Space b_p^(r,s) (D)

New Integrated and Differentiated Sequence Spaces ∫ b_p^(r,s) and db_p^(r,s)

New Sequence Spaces Derived by the Composition of Binomial and Quadruple Band Matrices

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