A-Statistical Convergence with a Rate and Applications to Approximation

Abstract

A =(ank) be a regular summability matrix. In the present paper we deal with subspaces of the space of A−statistically convergent sequences obtained by the rate at which the A−statistical limit goes to zero. We prove that a sequence is A−strongly convergent if and only if it is A−statistically convergent and A−uniformly integrable with the rate of o (an) where a=(an) is a positive nonincreasing sequence. We also make a link between A−strong convergence and A−distributional convergence with the rate of o (an). Finally, as an application we present an approximation theorem of Korovkin type.