Savaş, Ekrem2020-11-212020-11-2120170354-5180https://doi.org/10.2298/FIL1701069Shttps://hdl.handle.net/11467/390323rd International Conference on Finite and Infinite Dimensional Complex Analysis and Applications (ICFIDCAA) -- AUG 24-28, 2015 -- Kyushu Sangyo Univ, Fukuoka, JAPANWOS:000397267400009In this paper, we further generalize recently introduced summability methods in [23](where ideals of N were used to extend certain important summability methods) and introduce new notions, namely, I-statistical convergence of order alpha, where 0 < alpha < 1 by taking nonnegative real-valued Lebesque measurable function in the interval (1, infinity). We mainly investigate their relationship and also make some observations about these classes. The study leaves a lot of interesting open problems.eninfo:eu-repo/semantics/openAccessIdealfilterI-statistical convergence of order alphaI-lacunary statistical convergencenonnegative real-valued functionArticle3116976Q3WOS:000397267400009Q32-s2.0-8501227338910.2298/FIL1701069S