In this paper, we define and study the notion of lacunary statistical convergence and lacunary of statistical Cauchy sequences in random on Γ 3 over p-metric spaces defined by Musielak-Orlicz functions.

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.

We introduce and study some basic properties of rough I− convergent pre-Cauchy sequences of triple sequence of Bernstein polynomials and also study the set of all rough I− limits of a pre-Cauchy sequence of triple sequence of Bernstein polynomials and relation between analytic ness and rough I− statistical convergence of pre-Cauchy sequence of a triple sequences of Bernstein polynomials .

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Let Γ denote the space of all entire sequences and ∧ the space of all analytic sequences. This paper is devoted to the study of the general properties of Orlicz space ΓM of Γ

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<p>In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequence spaces. We define the set of Bernstein polynomials of rough statistical limit points of a triple sequence spaces and obtain to λ−statistical convergence criteria associated with this set. We examine the relation between the set of Bernstein polynomials of rough λ−statistically and ρ− Cauchy triple sequences.</p><p> </p><p> </p>

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