Inequalities for the Polar Derivative of a Polynomial
<p/> <p>Let <inline-formula> <graphic file="1029-242X-2009-515709-i1.gif"/></inline-formula> be a polynomial of degree <inline-formula> <graphic file="1029-242X-2009-515709-i2.gif"/></inline-formula> and for any real or complex numb...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2009/515709 |
| Summary: | <p/> <p>Let <inline-formula> <graphic file="1029-242X-2009-515709-i1.gif"/></inline-formula> be a polynomial of degree <inline-formula> <graphic file="1029-242X-2009-515709-i2.gif"/></inline-formula> and for any real or complex number <inline-formula> <graphic file="1029-242X-2009-515709-i3.gif"/></inline-formula>, and let <inline-formula> <graphic file="1029-242X-2009-515709-i4.gif"/></inline-formula> denote the polar derivative of the polynomial <inline-formula> <graphic file="1029-242X-2009-515709-i5.gif"/></inline-formula> with respect to <inline-formula> <graphic file="1029-242X-2009-515709-i6.gif"/></inline-formula>. In this paper, we obtain new results concerning the maximum modulus of a polar derivative of a polynomial with restricted zeros. Our results generalize as well as improve upon some well-known polynomial inequalities.</p> |
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| ISSN: | 1025-5834 1029-242X |