A Different Study on the Spaces of Generalized Fibonacci Difference bs and cs Spaces Sequence

Yaşar, Fevzi; Kayaduman, Kuddusi

doi:10.3390/sym10070274

Cited by 3 publications

(5 citation statements)

References 24 publications

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“…The spaces produced in some studies were the expansion of the original space while the others involved some overlap. For example, the space produced in the study of Yaşar and Kayaduman [38] is an expansion, while in this study, the space is a contraction. In this study, alpha, beta, and gamma duals of the spaces produced are available.…”

Section: Scope and Contributionmentioning

confidence: 79%

“…Yeşilkayagil and Başar [37] worked on the domain of the Nörlund matrix in some Maddox's spaces. Yaşar and Kayaduman [38] introduced and investigated sequence spaces bs(F(r, s)) and cs(F(r, s)) using the domain of the Generalized Fibonacci matrix on bs and cs. Furthermore, Mears [39,40] introduced some theorems and the inverse of the Nörlund matrix for the Nörlund mean.…”

Section: Literature Surveymentioning

confidence: 99%

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On Domain of Nörlund Matrix

Kayaduman

Yaşar²

2018

Mathematics

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In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space and and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α, β, γduals, and characterized their matrix transformations on this space and into this space.

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Section: Scope and Contributionmentioning

confidence: 79%

Section: Literature Surveymentioning

confidence: 99%

On Domain of Nörlund Matrix

Kayaduman

Yaşar²

2018

Mathematics

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“…For similar studies, see refeerences [19] and [27][28][29][30][31][32][33][34]. Let spaces cs(F) and bs(F) be the domain of the matrix F on cs and bs, where F = {f nk } infinite matrix is defined by (f n )…”

Section: The Domain Of Fibonacci Difference Matrix F On Bounded and Cmentioning

confidence: 99%

“…(17) R = (r nk ) ∈ (bv 0 , cs) iff Equations (10) and (43) hold [46]. Now, suppose v nk and v (m) nk which mentioned Equations (28) and (29) and give the following equations…”

Section: Lemma 17 [41]mentioning

confidence: 99%

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On the Domain of the Fibonacci Difference Matrix

Yaşar

Kayaduman

2019

Mathematics

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Matrix F̂ derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces lp(F) and l∞(F); (1 ≤ p < ∞) were examined. Then, Başarır et al. (2015) defined the spaces c0(F) and c(F) and Candan (2015) examined the spaces c(F(r,s)) and c0(F(r,s)). Later, Yaşar and Kayaduman (2018) defined and studied the spaces cs(F(s,r)) and bs(F(s,r)). In this study, we built the spaces cs(F) and bs(F). They are the domain of the matrix F on cs and bs, where F is a triangular matrix defined by Fibonacci Numbers. Some topological and algebraic properties, isomorphism, inclusion relations and norms, which are defined over them are examined. It is proven that cs(F) and bs(F) are Banach spaces. It is determined that they have the γ, β, α -duals. In addition, the Schauder base of the space cs(F) are calculated. Finally, a number of matrix transformations of these spaces are found.

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A New Aspect for Some Sequence Spaces Derived Using the Domain of the Matrix $\widehat{\widehat{B}}$

Candan

2022

Fundamental Journal of Mathematics and Applications

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This study serves for analysing algebraic and topological characteristics of the sequence spaces X( B(r, s)) constituted by using non-zero real number r and s, where X denotes arbitrary of the classical sequence spaces ∞ , c, c 0 and p (1 < p < ∞) of bounded, convergent, null and absolutely p-summable sequences, respectively and X( B) also is the domain of the matrix B(r, s) in the sequence space X. Briefly, the β -and γ-duals of the space X( B) are computed, and Schauder bases for the spaces c( B), c 0 ( B) and p ( B) are determined, and some algebraic and topological properties of the spaces c 0 ( B), 1 ( B) and p ( B) are studied. Additionally, it is observed that all these spaces have some remarkable features, including the classes (X 1 ( B): X 2 ) and (X 1 ( B) : X 2 ( B)) of infinite matrices which are characterized, in which X 1 ∈ { ∞ , c, c 0 , p , 1 } and X 2 ∈ { ∞ , c, c 0 , 1 }.

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A Different Study on the Spaces of Generalized Fibonacci Difference bs and cs Spaces Sequence

Cited by 3 publications

References 24 publications

On Domain of Nörlund Matrix

On Domain of Nörlund Matrix

On the Domain of the Fibonacci Difference Matrix

A New Aspect for Some Sequence Spaces Derived Using the Domain of the Matrix $\widehat{\widehat{B}}$

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