Virginia TechFenton, P. C.Rossi, John F.2014-07-212014-07-212002-02Fenton, P. C.; Rossi, J., "Growth of functions in cercles de remplissage," J. Austral. Math. Soc. 72 (2002), 131-136. DOI: 10.1017/S14467887000036451446-7887http://hdl.handle.net/10919/49641Suppose that f is meromorphic in the plane, and that there is a sequence z(n) --> infinity and a sequence of positive numbers epsilon(n) --> 0, such that epsilon(n)\z(n)f(#)(z(n))/log\z(n)\ --> infinity. It is shown that if f is analytic and non-zero in the closed discs Delta(n) = {z : \z - z(n)\ less than or equal to epsilon(n)\z(n)\}, n = 1, 2, 3,..., then, given any positive integer K, there are arbitrarily large values of n and there is a point z in Delta(n) such that \f(z)\ > \z\(K). Examples are given to show that the hypotheses cannot be relaxed.en-USIn CopyrightmathematicsArticle - Refereedhttp://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4831012&fulltextType=RA&fileId=S1446788700003645https://doi.org/10.1017/S1446788700003645