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  2. Nesbitt's inequality - Wikipedia

    en.wikipedia.org/wiki/Nesbitt's_inequality

    There is no corresponding upper bound as any of the 3 fractions in the inequality can be made arbitrarily large. It is the three-variable case of the rather more difficult Shapiro inequality, and was published at least 50 years earlier.

  3. Estimation lemma - Wikipedia

    en.wikipedia.org/wiki/Estimation_lemma

    In mathematics the estimation lemma, also known as the ML inequality, gives an upper bound for a contour integral. If f is a complex -valued, continuous function on the contour Γ and if its absolute value | f ( z ) | is bounded by a constant M for all z on Γ , then

  4. Inequality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inequality_(mathematics)

    For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < ⁠ 1 / 2 ⁠ and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < ⁠ 1 / 2 ⁠ .

  5. Shapiro inequality - Wikipedia

    en.wikipedia.org/wiki/Shapiro_inequality

    The special case with n = 3 is Nesbitt's inequality. For greater values of n the inequality does not hold, and the strict lower bound is γ ⁠ n / 2 ⁠ with γ ≈ 0.9891… (sequence A245330 in the OEIS). The initial proofs of the inequality in the pivotal cases n = 12 [2] and n = 23 [3] rely on numerical computations.

  6. Janson inequality - Wikipedia

    en.wikipedia.org/wiki/Janson_inequality

    In the mathematical theory of probability, Janson's inequality is a collection of related inequalities giving an exponential bound on the probability of many related events happening simultaneously by their pairwise dependence.

  7. Bernoulli's inequality - Wikipedia

    en.wikipedia.org/wiki/Bernoulli's_inequality

    Bernoulli's inequality can be proved for case 2, in which is a non-negative integer and , using mathematical induction in the following form: we prove the inequality for {,}, from validity for some r we deduce validity for +.

  8. Category:Statistical inequalities - Wikipedia

    en.wikipedia.org/wiki/Category:Statistical...

    Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more

  9. Weyl's inequality - Wikipedia

    en.wikipedia.org/wiki/Weyl's_inequality

    In linear algebra, Weyl's inequality is a theorem about the changes to eigenvalues of an Hermitian matrix that is perturbed. It can be used to estimate the ...

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