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Inequalities for the Polar Derivative of a Polynomial |
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| Authors: | A Liman R N Mohapatra W M Shah |
| Institution: | 1. Department of Mathematics, National Institute of Technology, Srinagar, Kashmir, 190006, India 2. Department of Mathematics, University of Central Florida, Orlando, FL, 32817, USA 3. Department of Mathematics, Kashmir University, Srinagar, 190006, India |
| Abstract: | Let P(z) be a polynomial of degree at most n. We consider an operator D ?? which maps a polynomial P(z) into D ?? P(z) :=?nP(z)?+?(?? ? z)P??(z) and prove results concerning the estimates of |D ?? P(z)| on the disk |z|?=?R??? 1, and thereby obtain extensions and generalizations of a number of well-known polynomial inequalities. |
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