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On strengthened Hardy and Pólya-Knopp’s inequalities. (English) Zbl 1034.26008
Summary: In this paper we prove a strengthened general inequality of the Hardy-Knopp type and also derive its dual inequality. Furthermore, we apply the obtained results to unify the strengthened classical Hardy and Pólya-Knopp’s inequalities deriving them as special cases of the obtained general relations. We discuss Pólya-Knopp’s inequality, compare it with Levin-Cochran-Lee’s inequalities and point out that these results are mutually equivalent. Finally, we also point out a reversed Pólya-Knopp type inequality.
MSC:
26D15Inequalities for sums, series and integrals of real functions