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Mursaleen introduced the concepts of statistical convergence in random 2-normed spaces. Recently Mohiuddine and Aiyup defined the notion of lacunary statistical convergence and lacunary statistical Cauchy in random 2-normed spaces. In this paper, we define and study the notion of lacunary statistical convergence and lacunary of statistical Cauchy sequences in random on χ over p− metric spaces defined by Musielak and prove some theorems which generalizes Mohiuddine and Aiyup results.

THE RANDOM OF LACUNARY STATISTICAL ON χ^2 OVER p− METRIC SPACES DEFINED BY MUSIELAK