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.).
2021
2021
MSC: Primary 40D25
Leonetti, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2142033
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