Generalized rough lacunary statistical triple difference sequence spaces in probability of fractional order defined by Musielak-Orlicz functionGeneralized rough lacunary statistical triple difference sequence spaces in probability of fractional order defined by Musielak-Orlicz function

Abstract

We generalized the concepts in probability of rough lacunary statistical by introducing the diference operator of fractional order, where is a proper fraction and = (mnk ) is anyxed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence and arbitrary sequence p = (prst) of strictly positive real numbers and investigate the topological structures of related triple diference sequence spaces. The main focus of the present paper is to generalized rough lacunary statistical of triple diference sequence spaces and investigate their topological structures as well as some inclusion concerning the operator :

Keywords

• analytic sequence
• Musielak-Orlicz function
• triple sequences
• chi sequence
• lacunary statistical convergence
• rough convergence