"A Two-Triangle Inequality", Daniel Pedoe, The American Mathematical Monthly, volume 70, number 9, page 1012, November, 1963.
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In geometry, Pedoe's inequality, named after Daniel Pedoe, states that if a, b, and c are the lengths of the sides of a triangle with area ƒ, and A, B, and C are the lengths of the sides of a triangle with area F, then
Daniel Pedoe | Inequality of bargaining power | gender inequality | Wirtinger's inequality | Steffensen's inequality | Samuelson's inequality | Minkowski inequality | Inequality for All | Hölder's inequality | Hitchin–Thorpe inequality | Fisher's inequality | Economic inequality | Chebyshev's sum inequality | Cauchy's inequality | Cauchy–Schwarz inequality |
In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.
A fundamental theorem, Fisher's inequality, named after the statistician Ronald Fisher, is that b ≥ v in any 2-design.
For 0 < p ≤ q ≤ ∞, the class Hq is a subset of Hp, and the Hp-norm is increasing with p (it is a consequence of Hölder's inequality that the Lp-norm is increasing for probability measures, i.e. measures with total mass 1).
Tristan Needham (1993) "A Visual Explanation of Jensen's Inequality", American Mathematical Monthly 100(8):768–71.
Steffensen's inequality and Steffensen's method (an iterative numerical method) are named after him.
Since the right-hand side of the identity is clearly non-negative, it implies Cauchy's inequality in the finite-dimensional real coordinate space ℝn and its complex counterpart ℂn.
The inequality in the above form was proved independently by Kullback, Csiszár, and Kemperman.
It is possible to determine the bounds of the roots of a polynomial using Samuelson's inequality.
: For other inequalities named after Wirtinger, see Wirtinger's inequality.