Tauberian theorems for iterations of methods of weighted arithmetic means

1978 ◽  
Vol 29 (3) ◽  
pp. 224-229
Author(s):  
N. A. Davydov
Keyword(s):  
Tauberian Theorems ◽  
Arithmetic Means ◽  
Weighted Arithmetic

Multivariable interpolation by weighted arithmetic means at arbitrary points

CALCOLO ◽  
1992 ◽  
Vol 29 (3-4) ◽  
pp. 301-311 ◽  
Author(s):  
G. Allasia ◽  
R. Besenghi ◽  
V. Demichelis
Keyword(s):  
Arithmetic Means ◽  
Weighted Arithmetic ◽  
Multivariable Interpolation

scholarly journals On Gauss compounding of symmetric weighted arithmetic means

2006 ◽  
Vol 322 (2) ◽  
pp. 729-734 ◽  
Author(s):  
Raghib Abu-Saris ◽  
Mowaffaq Hajja
Keyword(s):  
Arithmetic Means ◽  
Weighted Arithmetic

A Characterization of Weighted Arithmetic Means

1980 ◽  
Vol 1 (3) ◽  
pp. 259-260 ◽  
Author(s):  
J. Aczél ◽  
C. Wagner
Keyword(s):  
Arithmetic Means ◽  
Weighted Arithmetic

scholarly journals Maps Preserving Norms of Generalized Weighted Quasi-arithmetic Means of Invertible Positive Operators

2019 ◽  
Vol 35 ◽  
pp. 357-364
Author(s):  
Gergő Nagy ◽  
Patricia Szokol
Keyword(s):  
General Setting ◽  
Interesting Property ◽  
Positive Operators ◽  
Arithmetic Means ◽  
Mild Conditions ◽  
Weighted Arithmetic ◽  
The Common ◽  
Adjoint Operators

In this paper, the problem of describing the structure of transformations leaving norms of generalized weighted quasi-arithmetic means of invertible positive operators invariant is discussed. In a former result of the authors, this problem was solved for weighted quasi-arithmetic means, and here the corresponding result is generalized by establishing its solution under certain mild conditions. It is proved that in a quite general setting, generalized weighted quasi-arithmetic means on self-adjoint operators are not monotone in their variables which is an interesting property. Moreover, the relation of these means with the Kubo-Ando means is investigated and it is shown that the common members of the classes of these types of means are weighted arithmetic means.

Weighted arithmetic means possessing 0 the interpolation property

CALCOLO ◽  
1988 ◽  
Vol 25 (3) ◽  
pp. 203-217 ◽  
Author(s):  
G. Allasia ◽  
R. Besenghi ◽  
V. Demichelis
Keyword(s):  
Interpolation Property ◽  
Arithmetic Means ◽  
Weighted Arithmetic

Mean Entropies

2005 ◽  
Vol 12 (03) ◽  
pp. 289-302 ◽  
Author(s):  
B. H. Lavenda
Keyword(s):  
Probability Distribution ◽  
Generating Functions ◽  
Geometric Mean ◽  
Translation Invariance ◽  
Arithmetic Means ◽  
Mean Values ◽  
Weighted Arithmetic ◽  
Discrete Sample ◽  
The Mean ◽  
Increasing Functions

Entropies are expressed in terms of mean values, and not as weighted arithmetic means of their generating functions, which result in pseudo-additive entropies. The Shannon entropy corresponds to the logarithm of the inverse of the geometric mean, while the Rényi entropy, more generally, to the logarithm of the inverse of power means of order τ < 1. Translation invariance of the means relates to mean code lengths, while their homogeneity translates them into entropies: the arithmetic and exponential means correspond to the Shannon and Rényi entropies, respectively, under the Kraft equality. While under the Kraft inequality, the entropies are lower bounds to the mean code lengths. Means of any order cannot be expressed as escort averages because such averages contradict the fact that the means are monotonically increasing functions of their order. Exponential entropies are shown to be measures of the extent of a distribution. The probability measure and the incomplete probability distribution are shown to be the ranges of continuous and discrete sample spaces, respectively. Comparison is made with Boltzmann's principle.

On a Functional Equation Containing Weighted Arithmetic Means

2008 ◽  
pp. 305-315 ◽  
Author(s):  
Adrienn Varga ◽  
Csaba Vincze
Keyword(s):  
Functional Equation ◽  
Arithmetic Means ◽  
Weighted Arithmetic

Concavity of weighted arithmetic means with applications

1997 ◽  
Vol 69 (2) ◽  
pp. 120-126
Author(s):  
Arkady Berenstein ◽  
Alek Vainshtein
Keyword(s):  
Arithmetic Means ◽  
Weighted Arithmetic

scholarly journals Tauberian theorems for the statistical convergence and the statistical (C,1,1) summability

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Ümit Totur ◽  
İbrahim Çanak
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Convergent Sequence ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Difference Sequence ◽  
Arithmetic Means ◽  
The Difference ◽  
Single Sequence

Every P-convergent double sequence is statistically convergent and every bounded statistically convergent sequence is statistical (C,1,1) summable. The converse of these implications are not always true. Theorems on which conditioned converses are searched are known as Tauberian theorems. Inspired by the convergence to zero of the difference sequence between a sequence and its arithmetic means in the single sequence case, we obtain Tauberian theorems for the statistical convergence and statistical (C,1,1) summability method by imposing some conditions on the difference sequence between a double sequence and its different arithmetic means.

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