Inequality
111Linear inequality — In mathematics a linear inequality is an inequality which involves a linear function.Formal definitionsWhen operating in terms of real numbers, linear inequalities are the ones written in the forms: f(x) < b ext{ or }f(x) leq b,where f(x) is a… …
112Chebyshev's inequality — ▪ mathematics also called Bienaymé Chebyshev inequality in probability theory, a theorem that characterizes the dispersion of data away from its mean (average). The general theorem is attributed to the 19th century Russian mathematician… …
113Pedoe's inequality — 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 f , and A , B , and C are the lengths of the sides of a triangle with area F , then:A^2(b^2+c^2… …
114Lubell-Yamamoto-Meshalkin inequality — In combinatorial mathematics, the Lubell Yamamoto Meshalkin inequality, more commonly known as the LYM inequality, is an inequality on the sizes of sets in a Sperner family, proved by harvtxt|Bollobás|1965, harvtxt|Lubell|1966,… …
115Bernstein's inequality (mathematical analysis) — In the mathematical theory of mathematical analysis, Bernstein s inequality, named after Sergei Natanovich Bernstein, is defined as follows.Let P be a polynomial of degree n with derivative P prime; . Then:max(P ) le ncdotmax(P) where we define… …
116Bessel's inequality — In mathematics, especially functional analysis, Bessel s inequality is a statement about the coefficients of an element x in a Hilbert space with respect to an orthonormal sequence.Let H be a Hilbert space, and suppose that e 1, e 2, ... is an… …
117Gårding's inequality — In mathematics, Gårding s inequality is a result that gives a lower bound for the bilinear form induced by a real linear elliptic partial differential operator. The inequality is named after Lars Gårding.tatement of the inequalityLet Omega; be a… …
118Dvoretzky–Kiefer–Wolfowitz inequality — In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz inequality predicts how close an empirically determined distribution function will be to the distribution function from which the empirical samples are drawn. It is named …
119Kolgomorov's inequality — Kolmogorov s inequality is an inequality which gives a relation among a function and its first and second derivatives. Kolmogorov s inequality states the following:Let f colon mathbb{R} ightarrow mathbb{R} be a twice differentiable function on… …
120Bonnesen's inequality — is an inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetric inequality.More precisely, consider a planar simple closed curve …
