A new inequality for complex-valued polynomial functions

Rassias, Themistocles M.

doi:10.1090/S0002-9939-1986-0835884-9

A new inequality for complex-valued polynomial functions
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Proc. Amer. Math. Soc. 97 (1986), 296-298 Request permission

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 \[ {M_{{f_1}}}{M_{{f_2}}} \cdots {M_{{f_n}}} \geq {M_{{f_1}{f_2} \cdots {f_n}}} \geq k{M_{{f_1}}}{M_{{f_2}}} \cdots {M_{{f_n}}}\] where \[ k = {\left ( {\sin \frac {2}{n}\frac {\pi } {{8{d_1}}}} \right )^{{d_1}}}{\left ( {\sin \frac {2} {n}\frac {\pi }{{8{d_2}}}} \right )^{{d_2}}} \cdots {\left ( {\sin \frac {2}{n}\frac {\pi }{{8{d_n}}}} \right )^{{d_n}}}.\]

References

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