JournalszaaVol. 14, No. 1pp. 175–183

Gauss’ and Related Inequalities

  • S. Varošanec

    University of Zagreb, Croatia
  • J. Pečarić

    University of Zagreb, Croatia
Gauss’ and Related Inequalities cover
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Abstract

Let g:[a,b]Rg : [a,b] \to \mathbb R be a non-negative increasing differentiable function and f:[a,b]Rf : [a,b] \to \mathbb R a non-negative function such that the quotient f/gf/g’ is non-decreasing. Then the function

Q(r)=(r+1)abg(x)rf(x)dxQ(r) = (r+ 1) \int^b_a g(x)^r f(x)dx

is log-concave. If g(a)=0,b(a,]g(a) = 0, b \in (a, \infty] and the quotient f/gf/g’ is non-increasing, then the function QQ is log-convex.

Cite this article

S. Varošanec, J. Pečarić, Gauss’ and Related Inequalities. Z. Anal. Anwend. 14 (1995), no. 1, pp. 175–183

DOI 10.4171/ZAA/669