df-statistical convergence in connection with a modulus in metric spaces

Abstract

In this study we introduce -statistical convergence and -strong Cesaro summability with respect to a modulus for a sequence in a metric space. Furthermore we give the relations between the set of -statistically convergent sequences and the set of -strongly Cesaro summable sequences with respect to a modulus. Besides this we give the relations between the set of -strongly Cesaro summable and the set of -strongly Cesaro summable sequences in connection with a modulus.