GENERALIZATION OF SOME INEQUALITIES FOR THE POLAR DERIVATIVE OF POLYNOMIALS WITH RESTRICTED ZEROS

Autor:	Khojastehnezhad, Elahe, Bidkham, Mahmood
Jazyk:	angličtina
Předmět:	Inequality Restricted zeros High Energy Physics::Phenomenology Polar derivative High Energy Physics::Experiment Polynomial Inequality Maximum modulus Polar Derivative Restricted Ze- ros Polynomial Maximum modulus
Zdroj:	Volume: 9, Issue: 3 485-492 TWMS Journal of Applied and Engineering Mathematics
ISSN:	2146-1147 2587-1013
Popis:	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 = 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 = 1 except s-fold zeros at the origin. Publisher's Version
Databáze:	OpenAIRE
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