A Note on the $(\theta ,\varphi )$-Statistical Convergence of the Product Time Scale

Abstract

In this paper, we introduce the concepts $(\theta ,\varphi )$-density of a subset of the product time scale $\mathbb{T}^{2}$ and $(\theta ,\varphi )$ -statistical convergence of $\Delta $- measurable function $f$ \ defined on the product time scale $\mathbb{T}^{2}$ with the help of lacunary sequences. Later, we have discussed the connection between classical convergence and $ (\theta ,\varphi )$-statistical convergence. In addition, we have seen that $ f$ is strongly $(\theta ,\varphi )$-Cesaro summable on $\mathbb{T}^{2}$ then $f$ is $(\theta ,\varphi )$-statistical convergent$.$