Journal of the Ramanujan Mathematical Society

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A Generalization of A Theorem of Paul Turan


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1 Post-Graduate Department of Mathematics & Statistics University of Kashmir, Hazratbal, Singapur- 190 006, Kashmir, India
     

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If P(z) is a polynomial of degree n, then

Max|z|=1 |P(z)| ≤ n Max |z|=1 |P(z)|.

In (1) equality holds if and only if P[z) has all its zeros at the origin. Inequality (1) is an immediate consequence of S.Bernstein's theorem on the derivative of a Trigonometric Polynomial. (For reference see [2]).


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  • A Generalization of A Theorem of Paul Turan

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Authors

Wali Mohammad Shah
Post-Graduate Department of Mathematics & Statistics University of Kashmir, Hazratbal, Singapur- 190 006, Kashmir, India

Abstract


If P(z) is a polynomial of degree n, then

Max|z|=1 |P(z)| ≤ n Max |z|=1 |P(z)|.

In (1) equality holds if and only if P[z) has all its zeros at the origin. Inequality (1) is an immediate consequence of S.Bernstein's theorem on the derivative of a Trigonometric Polynomial. (For reference see [2]).