On the Derivative and Maximum Modulus Ofa Polynomial
نویسندگان
چکیده
The above inequality, which is an immediate consequence of Bernstein’s inequality on the derivative of a trigonometric polynomial, is best possible with equality holding for the polynomial p(z)= λzn, λ being a complex number. If we restrict ourselves to the class of polynomials having no zeros in |z| < 1, then the above inequality can be sharpened. In fact Erdös conjectured and later Lax [7] proved that if p(z) = 0 in |z| < 1, then
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