Summability factors between the absolute Cesàro methods

Özet

If Σ 􀀂􀀃􀀄􀀃 is summable by the method 􀀅 whenever Σ 􀀄􀀃 is summable by the method 􀀆, then we say that the factor 􀀂 = (􀀂􀀃) is of type (􀀆, 􀀅) and denote by (􀀆, 􀀅). In this study we characterize the sets (|􀀌, 􀀍|􀀎, |􀀌, −1|) , 􀀑 > 1 and (|􀀌, −1|, |􀀌, 􀀍|􀀎) , 􀀑 ≥ 1 for 􀀍 > −1. Also, in the special case, we give some inclusion relations between methods, which completes some open problems in literature.