Some inequalities for the polar derivative of a polynomial with restricted zeros

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1. A. Aziz and N. A. Rather, A refinement of a theorem of Paul Turan concerning polynomials, J. Math. Ineq. Appl, 1 (1998), 231-238.
2. A. Aziz, Inegualities for the polar derivative of a polynomial, J. Approx. Theory, 55 (1988), 183-193.
3. S. Bernstein, Leons sur les propri´et´es extr´emales et la meilleure approximation des fonctions analytiques d’une variable r´eelle. Gauthier Villars, Paris, 1926.
4. K. K. Dewan, J. Kaur and A. Mir, Inequalities for the derivative of a polynomial, J. Math. Anal. Appl, 269 (2002), 489-499.
5. K. K. Dewan, N. Singh and A. Mir, Growth of polynomials not vanishing inside a circle, Int. J. Math. Anal, 1 (2007), 529-538.
6. K. K. Dewn and C. M. Upadhye, Inequalities for the polar derivative of a polynomial, J. Inequal. Pure and Appl. Math, 9 (2008), 1-9.
7. N.K. Govil, On the derivative of a polynomial, Proc. Amer. Math. Soc, 41 (1973), 543-546.
8. A. Giroux, Q. I. Rahman and G. Schmeisser, On Bernstein’s inequality, Can. J. Math, 31 (1979), 347-353.
9. P. D. Lax, Proof of a conjecture of P. Erd¨os on the derivative of a polynomial, Bull. Amer. Math. Soc, 50 (1944), 509-513.
10. M. A. Malik, On the derivative of a polynomial, J. London. Math. Soc, 1 (1969), 57-60.
11. V. K. Jain, Generalization of certain well known inequalities for polynomial, Glas. Mat, 32 (1997), 45-51.
12. P. Turan, Uber die Ableitung von Polynomen, Compositio Math, 7 (1939), 89-95.