Let p(z) be a polynomial of degree n and for a complex number α, let Dαp(z) = np(z) + (α-z)p'(z) denote the polar derivative of the polynomial p(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all its zeros in
|z| ≤ K. Our results generalize and sharpen a famous inequality of Turn and some other known results in this direction.
and Orlicz spaces XΦ obtained by replacing the space L1 in the classical construction by an arbitrary Banach function space X. Our main aim is to focus on the task to study inequalities in such spaces. We prove a number of new inequalities and also
natural generalizations of some classical ones (e.g., Minkowski’s, H�lder’s and Young’s inequalities). Moreover, a number
of other basic facts for further study of inequalities and function spaces are included.
Authors:Péter Kórus, Luciano M. Lugo, and Juan E. Nápoles Valdés
REFERENCES  Dragomir , S. S. , Pečarić , J. and Persson , L. E. , Some inequalities of Hadamard Type , Soochow Journal of Mathematics, 21 ( 3 ), ( 1995 ), 335 – 341 .  Fleitas , A. , Méndez , J. A. , Nápoles Valdés , J. E