Comparison theorems between several quasi-arithmetic means

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-...

Mean-value Theorems for Multiplicative Arithmetic Functions of Several Variables

Let f : Nn → C be an arithmetic function of n variables, where n ≥ 2. We study the mean-value M(f) of f that is defined to be lim x1,...,xn→∞ 1 x1 · · ·xn ∑ m1≤x1, ... , mn≤xn f(m1, . . . , mn), if this limit exists. We first generalize the Wintner theorem and then consider the multiplicative case by expressing the mean-value as an infinite product over all prime numbers. In addition, we study ...

Weighted Quasi-Arithmetic Means: Utility Functions and Weighting Functions

An approach to Stochastic Process using Quasi-Arithmetic Means

Probability distributions are central tools for probabilistic modeling in data mining. In functional data analysis (FDA) they are weakly studied in the general case. In this paper we discuss a probability distribution law for functional data considered as stochastic process. We define first a new kind of stationarity linked t o the Archimedean copulas, and then we build a probability distributi...

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.