- Proceedings of International Mathematical Sciences
- Vol: 1 Issue: 1
- On the $\lambda _{h}^{\alpha }-$Statistical Convergence of the Functions Defined on the Time Scale
On the $\lambda _{h}^{\alpha }-$Statistical Convergence of the Functions Defined on the Time Scale
Authors : Name Tok, Metin Basarir
Pages : 1-10
View : 9 | Download : 5
Publication Date : 2019-06-15
Article Type : Research
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 $\alpha .$Keywords : delta-convergence, , statistical convergence, , density, , modulus function, time scale, Cesaro summable