Summability factors between the absolute Cesàro methods

Abstract

If Σε_{n}x_{n} is summable by the method Y whenever Σx_{n} is summable by the method X, then we say that the factor ε=(ε_{n}) is of type (X,Y) and denote by (X,Y). In this study we characterize the sets (|C,α|_{k},|C,-1|) , k>1 and (|C,-1|,|C,α|_{k}) , k≥1 for α>-1. Also, in the special case, we give some inclusion relations between methods, which completes some open problems in literature.