Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On two summability methods

Hüseyin Bora1

a1 Department of Mathematics, Erciyes University, Kayseri, Turkey

Let Σan be a given infinite series with partial sums sn, and rn = nan. By S030500410006268X_inline1 and S030500410006268X_inline2 we denote the nth Cesáro means of order α (α –1) of the sequences (sn) and (rn), respectively. The series Σan is said to be absolutely summable (C, a) with index k, or simply summable |C, α|k, k ≥ 1, if


(Received April 18 1984)

(Revised May 30 1984)


† Mail address: P. K. 213, Kayseri, Turkey