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- W4367325931 abstract "Let P(z) be a polynomial of degree n, then it is known that for $$alpha in {mathbb {C}}$$ with $$|alpha |le frac{n}{2},$$ $$begin{aligned} underset{|z|=1}{max }|left| zP^{prime }(z)-alpha P(z)right| le left| n-alpha right| underset{|z|=1}{max }|P(z)|. end{aligned}$$ This inequality includes Bernstein’s inequality, concerning the estimate for $$|P^prime (z)|$$ over $$|z|le 1,$$ as a special case. In this paper, we extend this inequality to $$L_p$$ norm which among other things shows that the condition on $$alpha $$ can be relaxed. We also prove similar inequalities for polynomials with restricted zeros." @default.
- W4367325931 created "2023-04-29" @default.
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- W4367325931 date "2023-04-12" @default.
- W4367325931 modified "2023-10-08" @default.
- W4367325931 title "Certain Bernstein-type $$L_p$$ inequalities for polynomials" @default.
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- W4367325931 doi "https://doi.org/10.1007/s44146-023-00074-x" @default.
- W4367325931 hasPublicationYear "2023" @default.
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