Summability factor relations between absolute weighted and Cesàro means

Abstract

By (U, V), we denote the set of all sequences 𝜖? = ?(𝜖n) such that ??nan is summable V whenever ?an is summable U, where U and V are two summability methods. Recently, Sarıgöl has characterized the set (Formula presented.) for k > 1,? > -1 and arbitrary positive sequences (Formula presented.) Now, in the present paper, we characterize the sets (Formula presented.), k > 1 and (Formula presented.), k ? 1 for arbitrary positive sequences (Formula presented.) Hence we extend these results to the range ?? - 1. In this way, some open problems in this topic are also completed. © 2018 John Wiley & Sons, Ltd.