Relation between summability and absolute summability by Cesàro means of complex order

I. I. Volkov

Moscow Institute of Agricultural Production Engineers

Abstract: It is proved that if a series is absolute summable by a Cesàro $(C,\alpha)$ method, then it is summable $(C,\beta)$ for any $\beta$, such that $\mathrm{Re}\,\alpha=\mathrm{Re}\,\beta>-1$.

UDC: 517.5

Received: 17.12.1969

 English version: Mathematical Notes, 1971, 9:1, 9–11

Bibliographic databases:

• 
•