On I-Lacunary Statistical Convergence of Weight g of Sequences of Sets

Abstract

In this paper, following a very recent
and new approach of \cite{BB} we further generalize
recently introduced summability methods in \cite{Ki} (where
ideals of $\mathbb{N}$ were used to extend certain important
summability methods) and introduce new notions, namely,
$\mathcal{I}$-statistical convergence of weight $g$ and $\mathcal{I}$-lacunary
statistical convergence of weight $g$, where $g : \mathbb{N} \rightarrow[0, \infty)$ is a function
satisfying $g\left( n \right) \to\infty$ and ${n \mathord{\left/
{\vphantom {n {g\left( n \right)}}} \right.
\kern-\nulldelimiterspace} {g\left( n \right)}}\nrightarrow0$
for sequences of sets. We mainly investigate their relationship and also make some
observations
about these classes. The study leaves a lot of interesting open problems