ON I-STATISTICAL AND I-LACUNARY STATISTICAL CONVERGENCE OF WEIGHT g

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, infinity) is a function satisfying g (n) -> infinity and n/g (n) negated right arrow 0. We mainly investigate their relationship and also make some observations about these classes. Our results extend the recent results of [7].