Some inequalities for the polar derivative of a polynomial |
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Authors: | Abdul Aziz Wali Mohammad Shah |
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Affiliation: | 1. Post-Graduate Department of Mathematics and Statistics, University of Kashmir, Hazratbal, 190 006, Srinagar, India
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Abstract: | LetP(z) be a polynomial of degreen which does not vanish in |z|<1. In this paper, we estimate the maximum and minimum moduli of thekth polar derivative ofP(z) on |z|=1 and thereby obtain compact generalizations of some known results, which among other results, yields interesting refinements of Erdos-Lax theorem and a theorem of Ankeny and Rivlin. |
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