Some inequalities for products of power sums

Research output: Contribution to journalArticlepeer-review


We study the asymptotic behavior of the range of the ratio of products of power sums. For x = (x1,…, xn), define Mp = Mp(x) = Σxip. As two representative and explicit results, we show that the maximum and minimum of the function M1M3/M22 are ±3√3/16n1/2 + 5/8 + O(n-1/2) and that n ≤ M1M3/M4 > -n/8, where "1/8" is the best possible constant. We give readily computable, if less explicit, formulas of this kind for Mp1a1 … Mprar/Mqb, Σa1p1 = bq. Applications to integral inequalities are discussed. Our results generalize the classical Hölder and Jensen inequalities. All proofs are elementary.

Original languageEnglish (US)
Pages (from-to)443-463
Number of pages21
JournalPacific Journal of Mathematics
Issue number2
StatePublished - Feb 1983

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Some inequalities for products of power sums'. Together they form a unique fingerprint.

Cite this