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

Authors : Name TOK, Metin BASARIR

Pages : 1-10

View : 16 | Download : 8

Publication Date : 2019-06-15

Article Type : Research Paper

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 $ $insert ignore into journalissuearticles values(0<\alpha \leq 1); $ of $\Delta -$ measurable function $f$ \ defined on the time scale $% \mathbb{T}$ with the help of modulus function $h$ and $\lambda =insert ignore into journalissuearticles values(\lambda _{n});$ 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