Vol. 33, No. 2, 1970

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Theorems on Cesàro summability of series

S. Mukhoti

Vol. 33 (1970), No. 2, 385–392
Abstract

1.1. We consider the Cesaro summability, for integral orders, of the series

∑∞
aνdν.
ν=0
(1.1)

In this paper we establish equivalence theorems for the series (1.1) which are valid for a substantial class of sequences dν including eν and νδ. Results of this character, but not overlapping with those in this paper, were given by Hardy and Littlewood and by Andersen. Andersen’s result was extended by Bosanquet and Chow, and further extended by Bosanquet.

Mathematical Subject Classification
Primary: 40.32
Milestones
Received: 12 January 1968
Revised: 29 January 1969
Published: 1 May 1970
Authors
S. Mukhoti