Generalization of some inequalities for the polar derivative of polynomials with restricted zeros
Künye
Khojastehnezhad, E. & Bidkham, M. (2019). Generalization of some inequalities for the polar derivative of polynomials with restricted zeros. TWMS Journal Of Applied And Engineering Mathematics, 9(3), 485-492.Özet
If p(z) is a polynomial of degree n, then Govil [N.K. Govil, Some inequalities for derivative of polynomials, J. Approx. Theory, 66 (1991) 29-35.] proved that if p(z) has all its zeros in vertical bar z vertical bar <= k, (k >= 1), then max(vertical bar z vertical bar=1) vertical bar P'(z)vertical bar >= 1 n/1 + k(n) {max(vertical bar z vertical bar=1) vertical bar P(z)vertical bar + min(vertical bar z vertical bar=1) vertical bar P(z)vertical bar} In this article, we obtain a generalization of above inequality for the polar derivative of a polynomial. Also we extend some inequalities for a polynomial of the form p(z) = z(s) (a(0) + Sigma(n-s)(v=t) a(nu)z(nu)), t >= 1, 0 <= s <= n - 1, which having no zeros in vertical bar z vertical bar < k, k >= 1 except s-fold zeros at the origin.
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http://belgelik.isikun.edu.tr/xmlui/handle/iubelgelik/2736http://jaem.isikun.edu.tr/web/index.php/archive/102-vol9no3/431
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