Some Aspects of Statistical Convergence and Cesàro Summability of Order $\alpha$ in Metric Spaces

Abstract

In the present paper, we extend the notions of $\rho$-statistically convergence and $\rho$-statistically boundedness of order $\alpha$ of scaler valued sequence to that of metric valued sequences from an arbitrary metric space $(X,d)$, where $\rho=(\rho_n)$ is a non decreasing sequence of positive real numbers. Beside this, we also generalize and study the notion of $\rho$-strongly Cesàro summability of order $\alpha$ for metric valued sequences. Finally we also demonstrate various inclusion relations among these concepts by varying the sequence $\rho=(\rho_n)$.