P. Leonetti

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20172022

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4 papers · 1 filter

math.CA2020

A Characterization of Cesaro Convergence

Paolo Leonetti

We show that a real bounded sequence $(x_{n})$ is Cesàro convergent to $ℓ$ if and only if the sequence of averages with indices in $[α^{k}, α^{k + 1})$ converges to $ℓ$ for all $α>1…

math.CA2020

Convergent subseries of divergent series

Marek Balcerzak, Paolo Leonetti

Let $X$ be the set of positive real sequences $x = (x_{n})$ such that the series $\sum_{n} x_{n}$ is divergent. For each $x \in X$ , let $I_{x}$ be the collectio…

math.CA2018

Convergence Rates of Subseries

Paolo Leonetti

Let $(x_{n})$ be a positive real sequence decreasing to $0$ such that the series $\sum_{n} x_{n}$ is divergent and $lim inf_{n} x_{n + 1} / x_{n} > 1/2$ . We show that there exists a constant $θ\…

math.CA2017

A Characterization of Convex Functions

Paolo Leonetti

Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f : D \to R \cup {+ \infty}$ is convex if and only if for all $…