On absolute generalized Hausdorff summability (Q1059236)

Hausdorff matrices have played an important role in summability theory and are intimately linked with the moment problem for a finite interval. The matrices of such standard methods of summability as the Cesàro, the Hölder, the Euler and the weighted mean methods are all Hausdorff or generalized Hausdorff matrices. In this paper we define the notion of absolute summability appropriate to generalized Hausdorff matrices and extend known results for ordinary Hausdorff matrices. In particular we establish relationships between generalized Cesàro and generalized Hölder absolute summability methods.