df-Statistical Convergence of Order $\alpha$ and df-Strong Cesaro Summability of Order $\alpha$ in Accordance to a Modulus in Metric Spaces

Rifat Colak, Emine Kayan

Abstract

In the current study we present df-statistical convergence of order $\alpha$ and df-strong Cesaro summability of order $\alpha$ in accordance to a modulus for a sequence ina metric space. Furthermore we introduce the connections between the sets of df-statistically convergent sequences of order $\alpha$ and between the sets of df-strongly Cesaro summable sequences of order $\alpha$ inaccordance to a modulus for various values $\alpha$ and under some conditions on f. Besides this we introduce the relationships between the set of df-statistically convergent sequences of order $\alpha$ and the set of df-strongly Cesaro summable sequences of order $\alpha$ inaccordance to a modulus for various values $\alpha$ and under some conditions on f.