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In this paper, some sharp inequalities for ordinary derivative $P'(z)$ and polar derivative $D_\alpha P(z)=nP(z)+(\alpha-z)P'(z)$ are obtained by including some of the coefficients and modulus of each individual zero of a polynomial $P(z)$ of degree $n$ not vanishing in the region $|z|>k$, $k\geq 1$. Our results also improve the bounds of Tur\'an's and Aziz's inequalities.
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참고문헌 (11)
참고문헌 신청
A. Aziz / 1983 / Inequalities for the derivative of a polynomial / Proc. Amer. Math. Soc 89:259~266
A. Aziz / 1998 / Inequalities for a polynomial and its derivatives / J. Approx. Theory 54:306~313
A. Aziz / 2004 / Some Zygmund type Lq inequalities for polynomials / J. Math. Anal. Appl 289:14~29
A. Aziz / 2003 / Inequalities for the polar derivative of a polynomial with restricted zeros / Math. Bulk 17:15~28
S. N. Bernstein / 1912 / Sur e'ordre de la meilleure approximation des functions continues par des polynomes de degre' donne' / Mem. Acad. R. Belg 12(4):1~103
A. Aziz / 1998 / Inequalities for a polynomial and its derivatives / J. Approx. Theory 54:306~313
A. Aziz / 2004 / Some Zygmund type Lq inequalities for polynomials / J. Math. Anal. Appl 289:14~29
A. Aziz / 2003 / Inequalities for the polar derivative of a polynomial with restricted zeros / Math. Bulk 17:15~28
S. N. Bernstein / 1912 / Sur e'ordre de la meilleure approximation des functions continues par des polynomes de degre' donne' / Mem. Acad. R. Belg 12(4):1~103
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