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, 14-20, 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 best-possible 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, 59-72, 1955). (Author)

Descriptors :   *HARMONIC ANALYSIS, FUNCTIONS(MATHEMATICS), INTEGRAL EQUATIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE