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On a Property of Rational Functions. II

1973
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Proceedings of the American Mathematical Society
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It is shown that if /-"(z) is a rational function of degree«such that/-"(0) = 1, lim|2|_,oc|i'"(z)|=0 and all its poles lie in |í1|^|z|^lthenmax|2|=p<|r1||rn(z)|^l/(l-p"). The example r*(z)= 1/(1 -zn) shows that (7) is sharp.

doi:10.2307/2038652
fatcat:zxsfwe5m7nal5mlnv3kxpdvoji