Computational Methods and Function Theory 5 (2005), No. 1, 1--17
Copyright Heldermann Verlag 2005
Stephen M. Zemyan
smz3@psu.edu , Department of Mathematics, Penn State Mont Alto, Mont Alto, PA 17237-9799, U.S.A.
In this paper, we introduce a new technique for measuring the hypothetical non-monotonicity of the argument of the vector tracing the omitted arc of a support point of the class S. It has been previously shown that the number of sign changes of arg(w(t))' on the omitted arc is finite. Here, we derive upper bounds for that number in terms of both the spherical and Schwarzian derivatives. Thus, our innovative approach identifies an inherently interesting connection between support point theory and these derivatives.
Keywords: Support point, omitted arc, wiggle point, waver point, spherical derivative, Schwarzian derivative, level set.
MSC 2000: Primary 30C45.
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