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In this paper, we introduce a class of summability methods that can be applied to lacunary double statistical convergence in topological groups and we also prove some theorems. [ABSTRACT FROM AUTHOR]

In this paper, following a very recent and new approach of [1], we further generalize recently introduced summability methods in [6] (where ideals of N were used to extend certain important summability methods) and introduce new notions, namely, I-statistical convergence of weight g and I-lacunary statistical convergence of weight g, where g : N → [0;∞) is a function satisfying g (n) → ∞ and n/g (n) → 0. We mainly investigate their relationship and also make some observations about these classes. Our results extend the recent results of [7]. [ABSTRACT FROM AUTHOR]