The purpose of this paper was to prove formally, using the Mizar language, Arithmetic Mean/Geometric Mean theorem known maybe better under the name of AM-GM inequality or Cauchy mean theorem. It states that the arithmetic mean of a list of a non-negative real numbers is greater than or equal to the geometric mean of the same list
The author proves almost wordlessly the Arithmetic Mean / Geometric Mean Inequality
Abstract: A new concept of exponential-geometric mean is introduced and its properties are analyzed....
AbstractRecently, Sagae and Tanabe defined a geometric mean of positive definite matrices and proved...
In this paper, we discuss some inequalities which are obtained by adding a non-negative expression t...
In the note, using Cauchy-Schwartz-Buniakowski's inequality, the authors give a new proof of the ari...
Discussing a series of inequalities, B. Bollobás reminds us in [3] that Harald Bohr wrote: “All ana...
In this paper we introduce a new mean which give new refinements\ud for AM-GM-HM inequalities, and w...
In the paper, we provide an alternative and united proof of a double in-equality for bounding the ar...
This article is the fourth in the ‘Inequalities’ series. This time, we present a novel proof of th...
There are many papers describing problems solved using the Boyer-Moore theorem prover, as well ass p...
In the current note, we investigate the mathematical relations among the weighted arithmetic mean&nd...
The purpose of this paper was to prove formally, using the Mizar language, Arithmetic Mean/Geometric...
Two families of means (called Heinz means and Heron means) that interpolate between the geometric an...
A version of this article appeared originally in the American Mathematical Monthly in 1981
We link some equivalent forms of the arithmetic-geometric mean inequality in probability and mathema...
The author proves almost wordlessly the Arithmetic Mean / Geometric Mean Inequality
Abstract: A new concept of exponential-geometric mean is introduced and its properties are analyzed....
AbstractRecently, Sagae and Tanabe defined a geometric mean of positive definite matrices and proved...
In this paper, we discuss some inequalities which are obtained by adding a non-negative expression t...
In the note, using Cauchy-Schwartz-Buniakowski's inequality, the authors give a new proof of the ari...
Discussing a series of inequalities, B. Bollobás reminds us in [3] that Harald Bohr wrote: “All ana...
In this paper we introduce a new mean which give new refinements\ud for AM-GM-HM inequalities, and w...
In the paper, we provide an alternative and united proof of a double in-equality for bounding the ar...
This article is the fourth in the ‘Inequalities’ series. This time, we present a novel proof of th...
There are many papers describing problems solved using the Boyer-Moore theorem prover, as well ass p...
In the current note, we investigate the mathematical relations among the weighted arithmetic mean&nd...
The purpose of this paper was to prove formally, using the Mizar language, Arithmetic Mean/Geometric...
Two families of means (called Heinz means and Heron means) that interpolate between the geometric an...
A version of this article appeared originally in the American Mathematical Monthly in 1981
We link some equivalent forms of the arithmetic-geometric mean inequality in probability and mathema...
The author proves almost wordlessly the Arithmetic Mean / Geometric Mean Inequality
Abstract: A new concept of exponential-geometric mean is introduced and its properties are analyzed....
AbstractRecently, Sagae and Tanabe defined a geometric mean of positive definite matrices and proved...
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