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

摘要

We generalized the concepts in probability of rough Ces$grave{a}$ro and lacunary statistical by introducing the difference operator $Delta^{lpha}_{gamma}$ of fractional order, where $lpha$ is a proper fraction and $gamma=left(gamma_{mnk}ight)$ is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence $heta$ and arbitrary sequence $p=left(p_{rst}ight)$ 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.