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Some Lower Bound Estimates for the Polar Derivatives of Polynomials with Restricted Zeros |
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PP: 1-5 |
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Author(s) |
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N. A. Rather,
A. Iqbal,
Ishfaq Dar,
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Abstract |
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| For a polynomial P(z) = zs(a0 +a1z+···+an−szn−s) ∈ Pn, 0 ≤ s ≤ n, it was shown recently by Rather et al. [12] that if P(z) ̸= 0 in |z| > k,k ≤ 1, then for every α ∈ C with |α| ≥ k,
max|DαP(z)|≥n|α|−k1+ ks+ kn−s|an−s|−|a0|max|P(z)|. |z|=1 1+k n kn−s|an−s|+|a0| |z|=1
In this paper, we obtain certain refinements of this inequality and related results. |
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