Statistical Convergence was introduced to solve problems of series summation. Many researchers gave many theories and results relating to Statistical Convergence in many spaces such as Statistical convergence on probabilistic normed space, Statistical convergence in Banach Spaces, Statistical Convergence on Normed Spaces, λ-Statistical Convergence, λ-Statistical Convergence of order α, Lacunary Statistical Convergence, Statistical convergence for Double Sequence, Statistical convergence of Double Sequences in Random 2-Normed Spaces, λ-Statistical Convergence of order α in Random 2-Normed Spaces etc.. In this work our purpose is to define λ - statistical convergence of order α in Random n-Normed space. Also examples are shown which shows the method is more generalized. Further we have defined Statistical Cauchy of order α in these spaces and prove Cauchy criterion in these spaces. Later, we have defined (λ,μ)- statistical convergence of order α∈[0,1), (V,λ,μ)- summability of order α for double sequence with the help of ideals. Also the example is given which shows this convergence does not hold good for( α) ̃>1.
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