Generalized Mean - Proof of Power Means Inequality

Proof of Power Means Inequality

We will prove weighted power means inequality, for the purpose of the proof we will assume without loss of generality that:

and

Proof for unweighted power means is easily obtained by substituting .

Read more about this topic:  Generalized Mean

Famous quotes containing the words proof of, proof, power, means and/or inequality:

    The proof of a poet is that his country absorbs him as affectionately as he has absorbed it.
    Walt Whitman (1819–1892)

    There is no better proof of a man’s being truly good than his desiring to be constantly under the observation of good men.
    François, Duc De La Rochefoucauld (1613–1680)

    There is a place where we are always alone with our own mortality, where we must simply have something greater than ourselves to hold onto—God or history or politics or literature or a belief in the healing power of love, or even righteous anger.... A reason to believe, a way to take the world by the throat and insist that there is more to this life than we have ever imagined.
    Dorothy Allison (b. 1949)

    Chief Justice. Your means are very slender, and your waste is great.
    Falstaff. I would it were otherwise. I would my means were greater, and my waist slenderer.
    William Shakespeare (1564–1616)

    All the aspects of this desert are beautiful, whether you behold it in fair weather or foul, or when the sun is just breaking out after a storm, and shining on its moist surface in the distance, it is so white, and pure, and level, and each slight inequality and track is so distinctly revealed; and when your eyes slide off this, they fall on the ocean.
    Henry David Thoreau (1817–1862)