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

Authors : Metin BASARIR

Pages : 192-196

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Publication Date : 2020-04-15

Article Type : Research Paper

Abstract :In this paper, we introduce the concepts $insert ignore into journalissuearticles values(\theta ,\varphi );$-density of a subset of the product time scale $\mathbb{T}^{2}$ and $insert ignore into journalissuearticles values(\theta ,\varphi );$ -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 $ insert ignore into journalissuearticles values(\theta ,\varphi );$-statistical convergence. In addition, we have seen that $ f$ is strongly $insert ignore into journalissuearticles values(\theta ,\varphi );$-Cesaro summable on $\mathbb{T}^{2}$ then $f$ is $insert ignore into journalissuearticles values(\theta ,\varphi );$-statistical convergent$.$
Keywords : delta convergence, statistical convergence, density, product time scale, lacunary sequences, p Cesaro summable