A-statistical convergence with a rate and applications to approximation

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