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Ky Fan inequality

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

21 relations: Arithmetic mean, Augustin-Louis Cauchy, Brouwer fixed-point theorem, Compact space, Concave function, Convex set, Edwin F. Beckenbach, Functional equation, Geometric mean, Inequality (mathematics), Inequality of arithmetic and geometric means, Jensen's inequality, Ky Fan, Levinson's inequality, Mathematics, Natural logarithm, Real number, Richard E. Bellman, Semi-continuity, Unit interval, Vector space.

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.

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Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 1789 – 23 May 1857) was a French mathematician reputed as a pioneer of analysis.

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Brouwer fixed-point theorem

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer.

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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).

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Concave function

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

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Convex set

In Euclidean space, a convex set is the region such that, for every pair of points within the region, every point on the straight line segment that joins the pair of points is also within the region.

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Edwin F. Beckenbach

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

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Functional equation

In mathematics, a functional equation is any equation that specifies a function in implicit form.

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Geometric mean

In mathematics, the geometric mean is a type of 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).

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Inequality (mathematics)

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

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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.

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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.

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Ky Fan

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

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Levinson's inequality

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

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Mathematics

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

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Natural logarithm

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

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Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

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Richard E. Bellman

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

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Semi-continuity

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

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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.

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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 in this context.

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References

[1] https://en.wikipedia.org/wiki/Ky_Fan_inequality

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