The invariance of the arithmetic mean with respect to generalized quasi-arithmetic means

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

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.

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...

Some Results on Lipschitz Quasi-Arithmetic Means

We present in this paper some properties of k-Lipschitz quasi-arithmetic means. The Lipschitz aggregation operations are stable with respect to input inaccuracies, what is a very important property for applications. Moreover, we provide sufficient conditions to determine when a quasi–arithemetic mean holds the k-Lipschitz property and allow us to calculate the Lipschitz constant k. Keywords— k-...

The Arithmetic - Harmonic Mean

Consider two sequences generated by ",,+ i Mi"„<hn)hn*\ M'i"„+X,b„), where the a„ and b„ are positive and M and M' are means. The paper discusses the nine processes which arise by restricting the choice of M and M' to the arithmetic, geometric and harmonic means, one case being that used by Archimedes to estimate it. Most of the paper is devoted to the arithmetic-harmonic mean, whose limit is e...