On factor relations between weighted and Nörlund means

Abstract

By (X, Y), we denote the set of all sequences o = (o n ) such that ?o n a n is summable Y whenever ?a n is summable X, where X and Y are two summability methods. In this study, we get necessary and sufficient conditions for o ?(|N, qn, u n | k, | N, p n |) and o ?(|N, p n |, | N, qn, u n | k ), k ? 1, using functional analytic tecniques, where | N, p n | and | N, qn, u n | k are absolute weighted and Nörlund summability methods, respectively, [1], [5]. Thus, in the special case, some well known results are also deduced. © 2019 Tamkang University. All Rights Reserved.