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 | Dimensione | Formato | |
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