Abstract
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 $\Delta^{\alpha}_{\gamma}.$
Highlights
A triple sequence can be defined as a function x : N × N × N → R (C), where N, R and C denote the set of natural numbers, real numbers and complex numbers respectively
The difference triple sequence space was introduced by Debnath et al and is defined as ∆xmnk = xmnk − xm,n+1,k − xm,n,k+1 + xm,n+1,k+1 − xm+1,n,k + xm+1,n+1,k + xm+1,n,k+1 − xm+1,n+1,k+1 and ∆0xmnk = xmnk
By using the operator ∆αγ, we introduce some new triple difference sequence spaces of rough Cesaro summable involving lacunary sequences θ and arbitrary sequence p = of strictly positive real numbers
Summary
A triple sequence (real or complex) can be defined as a function x : N × N × N → R (C) , where N, R and C denote the set of natural numbers, real numbers and complex numbers respectively. A triple sequence x = (xmnk) is said to be triple analytic if supm,n,k |xmnk| m+n+k < ∞. The space of all triple analytic sequences are usually denoted by Λ3. The notion of difference sequence spaces (for single sequences) was introduced by Kizmaz [6] as follows. The difference triple sequence space was introduced by Debnath et al (see [5]) and is defined as ∆xmnk = xmnk − xm,n+1,k − xm,n,k+1 + xm,n+1,k+1 − xm+1,n,k + xm+1,n+1,k + xm+1,n,k+1 − xm+1,n+1,k+1 and ∆0xmnk = xmnk
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Analysis and Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
