
Accession Number : AD0264867
Title : ON THE ARGUMENT OF THE DERIVATIVE OF A UNIVALENT FUNCTION
Corporate Author : UNIVERSITY COLL CORK (IRELAND)
Personal Author(s) : DONOHOE,P.J. ; KENNEDY,P.B.
Report Date : 20 MAR 1960
Pagination or Media Count : 1
Abstract : By consideration of an example due to Littlewood (On the Coefficients of Schlicht Functions, Quart. Jnl. Math. (1) 9, 1420, 1938) it is shown that, for functions f(z) regular and univalent in z < 1, the known estimate V(r,f) = 2o d arg f'(rei ) = 0(1)/(1  r) (as r 1) is bestpossible in the sense that V(r,f) > A/(1  r) for some function f of the class under consideration, some constant A > 0 and all sufficiently small 1  r > 0. This is an improvement on a result due to Flett (Some Remarks on Schlicht Functions and Harmonic Functions of Uniformly Sounded Variation, Quart. Jnl. Math. Oxford (2) 6, 5972, 1955). (Author)
Descriptors : *HARMONIC ANALYSIS, FUNCTIONS(MATHEMATICS), INTEGRAL EQUATIONS
Distribution Statement : APPROVED FOR PUBLIC RELEASE