?d -statistical convergence, ?d -statistical boundedness and strong (V, ?)d ?summability in metric spaces

Abstract

In this paper, we introduce and study ?d ?statistical convergence, ?d ?statistical boundedness and strong (V, ?)d ?summability of sequences in metric spaces. Furthermore we establish some relations between the sets of ?d -statistically convergent sequences, between the sets of ?d -statistically bounded sequences, between the sets of ?d ?statistical convergent sequences and the sets of strongly (V, ?)d ?summable sequences for various sequences ? = (?n) in ?. Furthermore we establish some inclusion relations between the sets of strongly (V, ?)d ?summable sequences for various sequences ? = (?n) in set ?? . © Springer Nature Singapore Pte Ltd. 2017.