On the maximum modulus of a polynomial and its polar derivative

摘要

For a polynomial p(z) of degree n, having all zeros in |z| ≤ 1, Jain is shown that mzx｜z｜=1｜D_α_1...Dα_1Dα_1P(z)｜≥n(n-1)…(n-t+1)/2t×1 {(|α_1|-1)…(|α_t|-1)}ma|p(z)| +｜z｜=1 {2~t (|α_1 | • • • |α_t|) - {(|α_1 | - 1) • • • (|α_t |-1)}} min |p(z)|] |z|=1, |α_1|≥ 1. |α_2| ≥ 1,… |α_t| ≥ 1, (t