On some Geometric Properties of Some Catalan Sequence Spaces

Objective & Hypothesis:It is important to know whether a Banach space is rotund or smooth when examining the structural properties of the space, especially its geometric properties.

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Key Findings & Data:In this study, we examined such properties of the sequence spaces $\ell _{p}(\widetilde{C}),$ $1\leq p<\infty ,$ and $\ell _{\infty }(\widetilde{C})$ constructed by the sequence of Catalan numbers.

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Conclusion & Impact:We have also shown that some types of these spaces have elite structural properties such as Approximation and Dunford-Pettis Properties.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Catalan numbers · approximation property · Dunford-Pettis property

Abstract

It is important to know whether a Banach space is rotund or smooth when examining the structural properties of the space, especially its geometric properties. Gateaux differentiability of the norm of the space has an important place in the discussion of smoothness. In this study, we examined such properties of the sequence spaces $\ell _{p}(\widetilde{C}),$ $1\leq p<\infty ,$ and $\ell _{\infty }(\widetilde{C})$ constructed by the sequence of Catalan numbers. We have also shown that some types of these spaces have elite structural properties such as Approximation and Dunford-Pettis Properties.

Keywords

Catalan numbers approximation property Dunford-Pettis property smoothness rotundity

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Cite This Article

Yılmaz, Y., Yalçın, S., Levent, H., Bozkurt, H. (2025). On some Geometric Properties of Some Catalan Sequence Spaces. Turkish Journal of Mathematics and Computer Science, Volume: 17 Issue: 2. https://doi.org/10.47000/tjmcs.1690548

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