The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (747 KB) | Metadata | Table of Contents | ZAA summary
Volume 14, Issue 1, 1995, pp. 175–183
DOI: 10.4171/ZAA/669

Published online: 1995-03-31

Gauss’ and Related Inequalities

S. Varošanec[1] and J. Pečarić[2]

(1) University of Zagreb, Croatia
(2) University of Zagreb, Croatia

Let $g : [a,b] \to \mathbb R$ be a non-negative increasing differentiable function and $f : [a,b] \to \mathbb R$ a non-negative function such that the quotient $f/g’$ is non-decreasing. Then the function $$Q(r) = (r+ 1) \int^b_a g(x)^r f(x)dx$$ is log-concave. If $g(a) = 0, b \in (a, \infty]$ and the quotient $f/g’$ is non-increasing, then the function $Q$ is log-convex.

Keywords: Gauss’ inequality, Popoviciu ’s inequality, Hölder’s inequality, log-concave functions, log-convex functions

Varošanec S., Pečarić J.: Gauss’ and Related Inequalities. Z. Anal. Anwend. 14 (1995), 175-183. doi: 10.4171/ZAA/669