We show that a real bounded sequence (Formula presented.) is Cesàro convergent to (Formula presented.) if and only if the sequence of averages with indices in (Formula presented.) converges to (Formula presented.) for all (Formula presented.). If, in addition, the sequence (Formula presented.) is nonnegative, then it is Cesàro convergent to 0 if and only if the same condition holds for some (Formula presented.).
A Characterization of Cesàro Convergence
Leonetti P
2021-01-01
Abstract
We show that a real bounded sequence (Formula presented.) is Cesàro convergent to (Formula presented.) if and only if the sequence of averages with indices in (Formula presented.) converges to (Formula presented.) for all (Formula presented.). If, in addition, the sequence (Formula presented.) is nonnegative, then it is Cesàro convergent to 0 if and only if the same condition holds for some (Formula presented.).
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
cesaro.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Creative commons
Dimensione
121.19 kB
Formato
Adobe PDF
|
121.19 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
