Certain topological properties for almost convergent Catalan-Motzkin sequence space

Authors : Muhammet Cihat Dağlı

Pages : 942-951

Doi:10.15672/hujms.1298097

View : 287 | Download : 396

Publication Date : 2024-08-27

Article Type : Research Paper

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