On a Property of Rational Functions. II

Q. I. Rahman
1973 Proceedings of the American Mathematical Society  
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