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, statement, classical and/or version:

    “After the first powerful plain manifesto
    The black statement of pistons, without more fuss
    But gliding like a queen, she leaves the station.”
    —Stephen Spender (1909–1995)

    “A sentence is made up of words, a statement is made in words.... Statements are made, words or sentences are used.”
    —J.L. (John Langshaw)

    “Several classical sayings that one likes to repeat had quite a different meaning from the ones later times attributed to them.”
    —Johann Wolfgang Von Goethe (1749–1832)

    “If the only new thing we have to offer is an improved version of the past, then today can only be inferior to yesterday. Hypnotised by images of the past, we risk losing all capacity for creative change.”
    —Robert Hewison (b. 1943)