Generalized Rough Cesaro and Lacunary Statistical Triple Difference Sequence Spaces in Probability of Fractional Order Defined by Musielak-Orlicz Function

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A. Esi, N. Subramanian


We generalized the concepts in probability of rough Ces$\grave{a}$ro and lacunary statistical by introducing the difference operator $\Delta^{\alpha}_{\gamma}$ of fractional order, where $\alpha$ is a proper fraction and $\gamma=\left(\gamma_{mnk}\right)$ is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence $\theta$ and arbitrary sequence $p=\left(p_{rst}\right)$ 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 generalized rough Ces$\grave{a}$ro and lacunary statistical of triple difference sequence spaces and investigate their topological structures as well as some inclusion concerning the operator $\Delta^{\alpha}_{\gamma}.$

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