On I-lacunary Statistical Convergence of Order α for Sequences of Sets

Abstract

In this paper, following a very recent and new approach of [1] and [2] we
further generalize recently introduced summability methods in [10] (where ideals of N
were used to extend certain important summability methods) and introduce new notions,
namely, I-statistical convergence of order α and I-lacunary statistical convergence of order
α, where 0 < α < 1 for sequences of sets. We mainly investigate their relationship
and also make some observations about these classes and in the way try to give a proof
of theorem which is not proved in [30]. The study leaves a lot of interesting open problems.