Abstract
We link some equivalent forms of the arithmetic-geometric mean inequality in probability and mathematical statistics.
Highlights
The arithmetic-geometric mean inequality in short, AG inequality has been widely used in mathematics and in its applications
A large number of its equivalent forms have been developed in several areas of mathematics
The purpose of this paper is to prove that the AG inequality is equivalent to some other renowned inequalities by using probabilistic arguments
Summary
The arithmetic-geometric mean inequality in short, AG inequality has been widely used in mathematics and in its applications. A large number of its equivalent forms have been developed in several areas of mathematics. For probability and mathematical statistics, the equivalent forms of the AG inequality have not been linked together in a formal way. The purpose of this paper is to prove that the AG inequality is equivalent to some other renowned inequalities by using probabilistic arguments. Among such inequalities are those of Jensen, Holder, Cauchy, Minkowski, and Lyapunov, to name just a few
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