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...

introducing Jensen's inequality, which was in turn named for work of Johan Jensen building on Hölder's work. The brief statement of Hölder's inequality uses...

in his spare time. Jensen is mostly renowned for his famous inequality, Jensen's inequality. In 1915, Jensen also proved Jensen's formula in complex analysis...

an interval of the real line. It generalizes the discrete form of Jensen's inequality, and generalizes in turn to the concept of Schur-convex functions...

Cauchy–Schwarz inequality. The AM–GM inequality is also known for the variety of methods that can be used to prove it. Jensen's inequality states that the...

squares of a 2 {\displaystyle a^{2}} and b 2 {\displaystyle b^{2}} . Jensen's inequality can also be proven graphically. A dashed curve along the X axis is...

)^{2}\right)}}=\sigma .\end{aligned}}} The first and third inequalities come from Jensen's inequality applied to the absolute-value function and the square...

known as Jensen's inequality, can be used to deduce inequalities such as the arithmetic–geometric mean inequality and Hölder's inequality. Let X {\displaystyle...

\ldots ,n} . The result can alternatively be proved using Jensen's inequality, the log sum inequality, or the fact that the Kullback-Leibler divergence is...

shown to be convex in [ 0 , S ] {\displaystyle [0,S]} and, invoking Jensen's inequality, we get a S − a + b S − b + c S − c 3 ≥ S / 3 S − S / 3 . {\displaystyle...