some compact generalization of inequalities for polynomials with prescribed zeros

Authors

h. a. soliman mezerji‎

freelance mathematics researcher‎, ‎mashhad‎, ‎iran. s. ahamadi

department of mathematics‎, ‎semnan university‎, ‎semnan‎, ‎iran. m. bidkham

department of mathematics‎, ‎semnan university‎, ‎semnan‎, ‎iran.

abstract

‎let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎in this paper we obtain some new results about the dependence of $|p(rz)|$ on $|p(rz)| $ for $r^2leq rrleq k^2$‎, ‎$k^2 leq rrleq r^2$ and for $rleq r leq k$‎. ‎our results refine and generalize certain well-known polynomial inequalities‎.

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Some compact generalization of inequalities for polynomials with prescribed zeros

‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

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Journal title:
bulletin of the iranian mathematical society

جلد ۴۳، شماره ۱، صفحات ۱۶۳-۱۷۰

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