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

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 in a 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 in accordance 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 in accordance to a modulus for various values alpha and under some conditions on f.