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In this paper we have introduced the concept of asymptotically double lacunary statistically equivalent of interval numbers and strong asymptotically double lacunary statistically equivalent of interval numbers. We have investigated the relations related to these spaces.

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Recently Savas and Das [12] introduced the notion of I -statistical convergence of sequences of real numbers. In this article we introduced the sequence spaces(M, A, p) and W I(S)∞ (M, A, p) of real numbers defined by I-statistical convergence using sequences of Orlicz function.We study some basic topological and algebraic properties of these spaces. We investigate some inclusion relations involving these spaces.

In this paper we have extended the concepts of I-limit superior and I-limit inferior to I-statistical limit superior and I-statistical limit inferior and studied some of their properties for sequence of real numbers.

In this paper, using the concept of natural density, we introduce the notion of rough statistical convergence of triple sequences. We define the set of rough statistical limit points of a triple sequence and obtain rough statistical convergence criteria associated with this set. Later, we prove this set is closed and convex and also examine the relations between the set of rough statistical cluster points and the set of rough statistical limit points of a triple sequence.

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