#### Glasnik Matematicki, Vol. 32, No.2 (1997), 213-215.

### AN *L*^{p} INEQUALITY FOR
SELF-INVERSIVE POLYNOMIALS

### N. K. Govil

Department of Mathematics, Auburn University, Auburn, AL 36849,
USA

**Abstract.** Let
denote the set of all polinomials *p*(*z*) of degree at
most *n*. Here we show that if *p*
and satisfies *p*(*z*) =
*z*^{n}*p*(1/*z*), then

*n*/2 ||*p*||_{δ}
||*p*'||_{δ}
*n* *C*_{δ}^{1/δ} ||*p*||_{δ},

where *C*_{δ} = (2^{-δ}
π
Γ(δ/2 + 1)) / (Γ(δ/2 + 1/2)).
The inequality on the right hand side is best possible and the equality
holds for polynomials *p*(*z*) =
*a* + *b**z*^{n}, |*a*| = |*b*|.
**1991 Mathematics Subject Classification.**
30A10, 30C10, 30E10.

**Key words and phrases.** Inequalities in the complex
domain, polynomials, approximation in the complex domain.

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