Power series methods and statistical limit superior

Abstract

Given a real bounded sequence x = (xj ) and an infinite matrix A = (anj ) the Knopp core theorem is equivalent to study the inequality lim sup Ax ≤ lim sup x. Recently Fridy and Orhan [6] have considered some variants of this inequality by replacing lim sup x with statistical limit superior st − lim sup x. In the present paper we examine similar type of inequalities by employing a power series method P, a non-matrix sequence-to-function trans- formation, in place of A = (anj ) .