Abstract
We generalized the concepts in the probability of rough lacunary statistical analysis of order η by introducing the difference operator Δ_γ^α of fractional order, where α is a proper fraction and γ=(γ_mnk ) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence θ and arbitrary sequence p=(p_rst ) of strictly positive real numbers and investigate the topological structures of related with triple difference sequence spaces. The main focus of the present paper is to generalize rough lacunary statistical analysis of order η of triple difference sequence spaces and give the relations between statistical analysis and lacunary statistical analysis of order η.
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