Das, P.Savaş, Ekrem2015-08-282015-08-2820141735-8515https://hdl.handle.net/11467/981In this paper, following a very recent and new approach, we further generalize recently introduced summability methods, namely, I-statistical convergence and I-lacunary statistical convergence (which extend the important summability methods, statistical convergence and lacunary statistical convergence using ideals of N) and introduce the notions of I-statistical convergence of order a and I-lacunary statistical convergence of order alpha, where 0 < alpha< 1. We mainly investigate their relationship and also make some observations about these classes and in the way try to give an answer to an open problem posed By Das, Savas and Ghosal in 2011. The study leaves a lot of interesting open problems.eninfo:eu-repo/semantics/openAccessIdeal; Filter; I-Statistical Convergence Of Order Alpha; I-Lacunary Statistical Convergence Of Order Alpha; Closed Subspace.ArticleQ4WOS:000341702400012N/A2-s2.0-84899749115