On Minkowski ’ s inequality and its application

  title={On Minkowski ’ s inequality and its application},
  author={Chang-Jian Zhao and Wing-Sum Cheung},
with equality if and only if f and g are proportional. For p <0, we assume that f(x), g (x) >0. An (almost) improvement of Minkowski’s inequality, for p Î R\{0}, is obtained in the following Theorem: Theorem 1.2 Let f(x), g(x) ≥ 0 and p >0, or f(x), g(x) >0 and p <0. Let s, t Î R\{0}, and s ≠ t. Then (i) Let p, s, t Î R be different, such that s, t >1 and (s t)/(p t) >1. Then ∫ (f (x)+g(x))pdx ≤ [(∫ f s(x)dx )1/s + (∫ gs(x)dx )1/s]s(p−t)/(s−t) 

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-5 of 5 references

Geometric Tomography

RJ Gardner
Cambridge University Press, New York • 1996
View 1 Excerpt

Convex Bodies: The Brunn-Minkowski Theory

R Schneider
Cambridge University Press, Cambridge • 1993
View 1 Excerpt

Intersection bodies and dual mixed volumes

E Lutwak
Adv Math. 71, 232–261 • 1988
View 1 Excerpt

Dual mixed volumes

E Lutwak
Pacific J Math. 58, 531–538 • 1975
View 2 Excerpts


GH Hardy, JE Littlewood, G Pólya
Cambridge University Press, Cambridge • 1934

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