Communication
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# Ky Fan inequality

In mathematics, there are two different results that share the common name of the Ky Fan inequality. [1]

## Aequationes Mathematicae

Aequationes Mathematicae is a mathematical journal.

## Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

## Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

## Brouwer fixed-point theorem

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer.

## Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

## Concave function

In mathematics, a concave function is the negative of a convex function.

## Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

## Edwin F. Beckenbach

Edwin Ford Beckenbach (18 July 1906 – 5 September 1982) was an American mathematician.

## Functional equation

In mathematics, a functional equation is any equation in which the unknown represents a function.

## Game theory

Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".

## Geometric mean

In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

## Inequality (mathematics)

In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).

## Inequality of arithmetic and geometric means

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same.

## Jensen's inequality

In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.

## Ky Fan

Ky Fan (樊,, September 19, 1914 &ndash; March 22, 2010) was an American mathematician and Emeritus Professor of Mathematics at the University of California, Santa Barbara (UCSB).

## Levinson's inequality

In mathematics, Levinson's inequality is the following inequality, due to Norman Levinson, involving positive numbers.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Richard E. Bellman

Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an American applied mathematician, who introduced dynamic programming in 1953, and important contributions in other fields of mathematics.

## Semi-continuity

In mathematical analysis, semi-continuity (or semicontinuity) is a property of extended real-valued functions that is weaker than continuity.

## Unit interval

In mathematics, the unit interval is the closed interval, that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1.

## Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

## References

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