Theorems on Cesàro summability of series

S. Mukhoti

Vol. 33 (1970), No. 2, 385–392

DOI: 10.2140/pjm.1970.33.385

Abstract

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

(1.1)

In this paper we establish equivalence theorems for the series (1.1) which are valid for a substantial class of sequences d_ν including e^−ν and ν^−δ. 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