Some Results on Lipschitz Quasi-Arithmetic Means
نویسندگان
چکیده
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-Lipschitz aggregation functions, quasi-arithmetic means, stability, triangular norms.
منابع مشابه
On Lipschitz properties of generated aggregation functions
This article discusses Lipschitz properties of generated aggrega-tion functions. Such generated functions include triangular norms and conorms, quasi-arithmetic means, uninorms, nullnorms and continuous generated functions with a neutral element. The Lipschitz property guarantees stability of aggregation operations with respect to input inaccuracies, and is important for applications. We provid...
متن کاملOn 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.
متن کاملA remark on the means of the number of divisors
We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$, where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$, with $d(n)$ denoting the number of positive divisors of $n$. Also, we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.
متن کاملQuasi-arithmetic means of covariance functions with potential applications to space-time data
The theory of quasi-arithmetic means is a powerful tool in the study of covariance functions across space-time. In the present study we use quasiarithmetic functionals to make inferences about the permissibility of averages of functions that are not, in general, permissible covariance functions. This is the case, e.g., of the geometric and harmonic averages, for which we obtain permissibility c...
متن کاملOn Some Classes of Aggregation Functions that are Migrative
In this paper we introduce and describe two classes of aggregation functions with members that are migrative. First continuous triangular norms are studied that own the migrative property with respect to another fixed t-norm, in particular to the three prototypes minimum, product, and the Łukasiewicz t-norm. For classes of nilpotent and strict migrative t-norms the characterization and construc...
متن کامل