On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale

Authors : Bayram SÖZBİR, Selma ALTUNDAĞ, Metin BASARIR

Pages : 138-143

Doi:10.32323/ujma.743949

View : 18 | Download : 8

Publication Date : 2020-12-23

Article Type : Research Paper

Abstract :In this paper, we first define a new density of a $\Delta $-measurable subset of a product time scale ${\Lambda ^2}$ with respect to an unbounded modulus function. Then, by using this definition, we introduce the concepts of $\Delta _{{\Lambda ^2}}^f$-statistical convergence and $\Delta _{{\Lambda ^2}}^f$-statistical Cauchy for a $\Delta $-measurable real-valued function defined on product time scale ${\Lambda ^2}$ and also obtain some results about these new concepts. Finally, we present the definition of strong $\Delta _{{\Lambda ^2}}^f$-Cesaro summability on ${\Lambda ^2}$ and investigate the connections between these new concepts.
Keywords : Delta measure, Density, Modulus function, Product time scale, Statistical convergence, Strong Cesaro summability