Generalization of some polynomial inequalities not vanishing in a disk |
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Authors: | Sunil Hans Roshan Lal |
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Institution: | 1. Department of Applied Science, ITM University, Gurgaon, India, 122017 2. Department of Mathematics, Govt. Degree College, Chaubattakhal (Pauri), Uttarakhand, India
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Abstract: | If $P(z) = \sum\limits_{\nu = 0}^n {c_\nu z^\nu } $ is a polynomial of degree n, then for |β| ≤ 1, it was proved in 4] that $\left| {zP'(z) + n\frac{\beta } {2}P(z)} \right| \leqslant n\left| {1 + \frac{\beta } {2}} \right|\mathop {\max }\limits_{|z| = 1} |P(z)|,|z| = 1 $ In this paper, first we generalize the above result for the s th derivative of polynomials and next we improve the above inequality for polynomials with restricted zeros. |
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