An invariance of geometric mean with respect to generalized quasi-arithmetic means

Invariance of a quasi-arithmetic mean with respect to a system of generalized Bajraktarević means

Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters

In the article, we present the best possible parameters [Formula: see text] and [Formula: see text] on the interval [Formula: see text] such that the double inequality [Formula: see text] holds for any [Formula: see text] and all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic, geometric and special quasi-ar...

Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean

In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two posi...

On Hadamard Type Inequalities for Generalized Weighted Quasi-arithmetic Means

In the present paper we establish some integral inequalities analogous to the wellknown Hadamard inequality for a class of generalized weighted quasi-arithmetic means in integral form.

Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means

Copyright q 2010 B.-Y. Long and Y.-M. Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For p ∈ R, the generalized logarithmic mean L p a, b, arithmetic mean Aa, b, and geometric mean Ga, b of two positive numbers a and b are d...