Some triple difference rough Cesàro and lacunary statistical sequence spaces

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