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– 268 . [2] A lzer , H. and K wong , M. K. , On Young's inequality , J. Math. Anal. Appl. , 469 ( 2019 ), 480 – 492 . [3

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Abstract  

Let p(z) be a polynomial of degree n and for a complex number α, let D α p(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.

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Abstract  

We discuss and complement the knowledge about generalized Orlicz classes
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde X_\Phi$$ \end{document}
and Orlicz spaces X Φ obtained by replacing the space L 1 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.
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. , Mean Value Inequalities for Convex and Starshaped Sets, Aequationes Mathematicae , Vol. 70(3) (2005), 213–224. MR 2007c :52008 Slodkowski Z. Mean Value Inequalities for

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. [2] Dawson , D. and Sankoff , D. , An inequality for probabilities , Proc. Amer. Math. Soc. , 18 ( 1967 ), 504 - 507 . [3

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Crespi, G., Ginchev, I. and Rocca, M. , Minty variational inequalities, increase-along-rays property and optimization, J. Optimization Theory Appl. , 123 (2004), 479–496. MR 2005i

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REFERENCES [1] Dragomir , S. S. , Pečarić , J. and Persson , L. E. , Some inequalities of Hadamard Type , Soochow Journal of Mathematics, 21 ( 3 ), ( 1995 ), 335 – 341 . [2] Fleitas , A. , Méndez , J. A. , Nápoles Valdés , J. E

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Alomari, M. and Darus, M. , On The Hadamard’s inequality for log-convex functions on the coordinates, J. Inequal. Appl. , 2009 (2009), Article ID 283147, 13 pages; Available online at http

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