Certain topological properties for almost convergent Catalan-Motzkin sequence space

Year 2024, Early Access, 1 - 10

Muhammet Cihat Dağlı

https://doi.org/10.15672/hujms.1298097

Abstract

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.

Keywords

Catalan numbers, almost convergence, sequence spaces, core theorems

References

• [1] B. Altay, F. Başar and E. Malkowsky, Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness, Appl. Math. Comput. 211, 255–264, 2009