Inclusion relations between the statistical convergence and strong summability

Abstract

For a sequential method of summability B we define B-density and B-statistical convergence in a Banach space X, and investigate inclusion relations between the space of B-statistically convergent sequences and the space of strongly B-summable sequences with respect to a sequence of modulus functions F=(f_k). As an application, two theorems of Pehlivan and Fisher [27] are corrected.