I−Lacunary Summability Function of Order α

Abstract

In this paper, we further generalize recently introduced
summability methods in \cite{CC}(where ideals of $\mathbb{N}$ were
used to extend certain important summability methods) and
introduce new notions, namely, $\mathcal{I-}$statistical
convergence of order $\alpha$, where $0<\alpha<1$ by taking
nonnegative real-valued Lebesque measurable function in the
interval $(1,\infty).$ We mainly investigate their relationship
and also make some observations about these classes. The study
leaves a lot of interesting open problems.