Some topologic and geometric properties of new Catalan sequence spaces

Karakaş, Murat; Dağli, Muhammet Cihat

doi:10.1007/s43036-022-00243-9

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

2024

Publication Types

Select...

Article4

Relationship

Self Cite0

Independent4

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Motivated by another representation of Catalan numbers, given by (1.1), Karakas and Dağlı [37] presented a new conservative matrix C = (c nk ) as…”

Section: Introductionmentioning

confidence: 99%

Certain topological properties for almost convergent Catalan-Motzkin sequence space

DAĞLI

2023

Hacettepe Journal of Mathematics and Statistics

View full text Add to dashboard Cite

The purpose of this paper is to introduce a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the beta- dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.

show abstract

“…Motivated by another representation of Catalan numbers, given by (1.1), Karakas and Dağlı [37] presented a new conservative matrix C = (c nk ) as…”

Section: Introductionmentioning

confidence: 99%

Certain topological properties for almost convergent Catalan-Motzkin sequence space

DAĞLI

2023

Hacettepe Journal of Mathematics and Statistics

View full text Add to dashboard Cite

show abstract

On the paranormed sequence space arising from Catalan–Motzkin matrix

Dağli

2023

Adv. Oper. Theory

View full text Add to dashboard Cite

Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space

DEMİRİZ,

ERDEM

2024

Communications in Advanced Mathematical Sciences

View full text Add to dashboard Cite

In this study, it is introduced the regular Mersenne matrix operator which is obtained by using Mersenne numbers and examined sequence spaces described as the domain of this matrix in the space of $p$-summable sequences for $1\leq p \leq \infty$. After that, it investigated some properties and inclusion relations, established the Schauder basis, and stated $\alpha-$, $\beta-$, and $\gamma-$duals of the aforementioned spaces. Additionally, it is characterized by the matrix classes from newly described spaces to classical sequence spaces. Finally, we studied the compactness of matrix operators on related sequence spaces.

show abstract

Some topologic and geometric properties of new Catalan sequence spaces

Cited by 4 publications

References 39 publications

Certain topological properties for almost convergent Catalan-Motzkin sequence space

Certain topological properties for almost convergent Catalan-Motzkin sequence space

On the paranormed sequence space arising from Catalan–Motzkin matrix

Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space

Contact Info

Product

Resources

About