On the $\lambda _{h}^{\alpha }-$Statistical Convergence of the Functions Defined on the Time Scale

Abstract

In this paper, we have introduced the concepts $\lambda _{h}^{\alpha }$% -density of a subset of the time scale $\mathbb{T}$ and $\lambda _{h}^{\alpha }$-statistical convergence of order $\alpha $ $(0<\alpha \leq 1) $ of $\Delta -$ measurable function $f$ \ defined on the time scale $% \mathbb{T}$ with the help of modulus function $h$ and $\lambda =(\lambda _{n})$ sequences. Later, we have discussed the connection between classical convergence, $\lambda $-statistical convergence and $\lambda _{h}^{\alpha }$% -statistical convergence. In addition, we have seen that $f$ is strongly $% \lambda _{h}^{\alpha }$-Cesaro summable on T then $f$ is $\lambda _{h}^{\alpha }$-statistical convergent of order $\alpha .$