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) .