Power series methods and statistical limit superior

Abstract

Given a real bounded sequence x = ( x j ) and an infinite matrix A = ( a n j ) Knopp core theorem is equivalent to study the inequality l i m s u p A x ≤ l i m s u p x . Recently Fridy and Orhan [6] have considered some variants of this inequality by replacing l i m s u p x with statistical limit superior s t − l i m s u p x . In the present paper we examine similar type of inequalities by employing a power series method P ; a non-matrix sequence-to-function transformation, in place of A = ( a n j ) .