Power series methods and statistical limit superior

Given a real bounded sequence $x=(x_{j})$ and an infinite matrix $A=(a_{nj})$ Knopp core theorem is equivalent to study the inequality $limsup{Ax} ≤ limsup{x}.$ Recently Fridy Orhan [6] have considered some variants of this by replacing $limsup{x}$ with statistical limit superior $st - limsup{x}$. In present paper we examine similar type inequalities employing power series method $P$; non-matrix sequence-to-function transformation, in place $A =(a_{nj})$ .