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Öğe On I-Statistical And I-Lacunary Statistical Convergence Of Order Alpha(Iranian Mathematical Soc., 2014) Das, P.; Savaş, EkremIn 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.Öğe On I-Statistically Order Pre Cauchy Sequences in Riesz Spaces(Springer, 2020) Das, P.; Savaş, EkremIn this paper. we continue to investigate in line of the recent work of Sencimen and Pehlivan, Das and Savas and consider the notion of -statistical order pre Cauchy condition related to a new type of order convergence, namely -statistical order convergence in Riesz spaces and establish some of its basic properties. We mainly investigate their inter-relationship. © 2020, Springer Nature Singapore Pte Ltd.