Mean Value Problem

(Unsolved Problems In Mathematic)

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Unsolved Problems In Mathematic
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What is Mean value problem?

In mathematics, the mean value problem was posed by Stephen Smale in 1981. This problem is still open in full generality. The problem asks: For a given complex polynomial of degree and a complex number , is there a critical point of (i.e. ) such that It was proved for . For a polynomial of degree the constant has to be at least from the example , therefore no bound better than can exist. Gerald Schmieder published a paper in 2003 where he claims to have proven the theorem for this optimal bound of .

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