Inscription on statistical convergence of order $\alpha$

Abstract

In this article we epitomize a remarkable result stated as "\emph{For a fixed $\alpha,$ $0<\alpha \leq 1,$ the set of all bounded statistically convergent sequences of order $\alpha$ is a closed linear subspace of $m$ (m is the set of all bounded real sequences endowed with the sup norm)}" by Bhunia et al. (Acta Math. Hungar.  130 (1-2) (2012), 153--161) and to elevate the objective of this perception we exhibit that the set of all bounded statistically convergent sequences of order $\alpha$ may not form a closed subspace in other sequence spaces. Also we adorn two different sequence spaces in which the set of all statistically convergent sequences of order $\alpha$ (irrespective of boundedness) forms a closed set.