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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new inequality for complex-valued polynomial functions


Author: Themistocles M. Rassias
Journal: Proc. Amer. Math. Soc. 97 (1986), 296-298
MSC: Primary 30A10; Secondary 30C10
MathSciNet review: 835884
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Abstract: Let $ {f_1},{f_2}, \ldots ,{f_n}:{\mathbf{C}} \to {\mathbf{C}}$ be complex-valued polynomial functions of degrees $ {d_1},{d_2}, \ldots ,{d_n}$, respectively, of a complex variable $ z$. Then

$\displaystyle {M_{{f_1}}}{M_{{f_2}}} \cdots {M_{{f_n}}} \geq {M_{{f_1}{f_2} \cdots {f_n}}} \geq k{M_{{f_1}}}{M_{{f_2}}} \cdots {M_{{f_n}}}$

where

$\displaystyle k = {\left( {\sin \frac{2}{n}\frac{\pi } {{8{d_1}}}} \right)^{{d_... ...d_2}}} \cdots {\left( {\sin \frac{2}{n}\frac{\pi }{{8{d_n}}}} \right)^{{d_n}}}.$


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0835884-9
PII: S 0002-9939(1986)0835884-9
Keywords: Complex polynomial function, connected subset, length, inequalities
Article copyright: © Copyright 1986 American Mathematical Society