Ky Fan Inequality - Statement of The Classical Version

Statement of The Classical Version

If xi with 0 ≤ xi ≤ ½ for i = 1, ..., n are real numbers, then

\frac{ \bigl(\prod_{i=1}^n x_i\bigr)^{1/n} } { \bigl(\prod_{i=1}^n (1-x_i)\bigr)^{1/n} } \le \frac{ \frac1n \sum_{i=1}^n x_i } { \frac1n \sum_{i=1}^n (1-x_i) }

with equality if and only if x1 = x2 = . . . = xn.

Read more about this topic:  Ky Fan Inequality

Famous quotes containing the words statement of the, statement of, statement, classical and/or version:

    “Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual’s sovereignty.”
    —Mario Vargas Llosa (b. 1936)

    “Most personal correspondence of today consists of letters the first half of which are given over to an indexed statement of why the writer hasn’t written before, followed by one paragraph of small talk, with the remainder devoted to reasons why it is imperative that the letter be brought to a close.”
    —Robert Benchley (1889–1945)

    “Most personal correspondence of today consists of letters the first half of which are given over to an indexed statement of why the writer hasn’t written before, followed by one paragraph of small talk, with the remainder devoted to reasons why it is imperative that the letter be brought to a close.”
    —Robert Benchley (1889–1945)

    “Against classical philosophy: thinking about eternity or the immensity of the universe does not lessen my unhappiness.”
    —Mason Cooley (b. 1927)

    “Remember that you were a slave in the land of Egypt, and the LORD your God brought you out from there with a mighty hand and an outstretched arm; therefore the LORD your God commanded you to keep the sabbath day.”
    —Bible: Hebrew, Deuteronomy 5:15.

    See Exodus 22:8 for a different version of this fourth commandment.