ACTA issues

Some new observations on Catalan almost convergent sequence spaces and the Catalan core

Swati Jasrotia, Uday Pratap Singh, Kuldip Raj

Acta Sci. Math. (Szeged) 87:1-2(2021), 153-163

Abstract. In this article, we introduce and study Catalan almost convergent sequence spaces by using the Catalan matrix. We obtain topological properties and the $\beta $-dual of the resulting sequence spaces. Finally, we define the Catalan core of complex-valued sequences and give some inclusion theorems related to the Catalan core.

DOI: 10.14232/actasm-020-793-6

AMS Subject Classification (1991): 40A05, 40A30

Keyword(s): Catalan numbers, almost convergence, sequence spaces, core theorems

received 12.10.2020, revised 21.1.2021, accepted 30.1.2021. (Registered under 43/2020.)