Yılmaz, YılmazYalçın, SeçkinLevent, HaliseBozkurt, Hacer2026-04-042026-04-0420252148-1830https://doi.org/10.47000/tjmcs.1690548https://search.trdizin.gov.tr/tr/yayin/detay/1375567https://hdl.handle.net/11616/108206It 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 ℓp (˜C), 1 ≤ p < ∞, and ℓ∞(˜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. © MatDer.eninfo:eu-repo/semantics/openAccessapproximation propertyCatalan numbersDunford-Pettis propertyrotunditysmoothnessArticle17248549510.47000/tjmcs.16905482-s2.0-105027683000Q41375567