Generalized Asymptotically I-Lacunary Statistical Equivalent of Order α for Sequences of Sets

Abstract

In this paper we present , for sequences of sets, the concept of generalized asymptotically $\mathcal{I}$-lacunary statistical equivalent of order $\alpha$, ($0<\alpha \leq 1$),
to multiple $L$, where $I$ is an
ideal of the subset of $\mathbb{N}$. In addition to
this definition inclusion theorems are also presented. The study leaves some interesting open problems