On Copson’s inequalities for \(0< p<1\). (English) Zbl 1503.26049
Summary: Let \((\lambda_n)_{n \geq1}\) be a positive sequence and let \(\varLambda_n=\sum^n_{i=1}\lambda_i\). We study the following Copson inequality for \(0< p<1, L>p\):
\[\sum^{\infty}_{n=1} \left(\frac{1}{\varLambda_n} \sum^{\infty }_{k=n}\lambda_k x_k \right)^p \geq \left( \frac{p}{L-p} \right)^p \sum^{\infty}_{n=1}x^p_n.\]
We find conditions on \(\lambda_n\) such that the above inequality is valid with the constant being the best possible.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
Keywords:
Copson inequalitiesReferences:
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