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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.)
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