Some inequalities involving integral means. (English) Zbl 1164.26015

Haluška, Ján; Hutník, Ondrej

Tatra Mt. Math. Publ. 35, 131-146 (2007).

The generalized weighted quasi-arithmetic means of a function with respect to weight functions are introduced, and some examples of weighted means are given.
Moreover, some generalized versions of the Jensen inequality are proved, relatively to such means.
Some other more general inequalities are presented and demonstrated, and some examples and applications are given.

Reviewer: Antonio Boccuto (Perugia)

MSC:

26D10

Inequalities involving derivatives and differential and integral operators

Keywords:

generalized weighted mean; quasi-arithmetic mean; integral mean; Jensen’s inequality; convex function