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Starlike Univalent Functions Bounded on the Real Axis

Published online by Cambridge University Press:  20 November 2018

Richard Fournier
Richard Fournier*
Affiliation:
Université de Montréal, Montréal, Québec
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We denote by E the open unit disc in C and by H(E) the class of all analytic functions f on E with f(0) = 0. Let (see [3] for more complete definitions)

S = {ƒ ∈ H(E)|ƒ is univalent on E}

S0 = {ƒ ∈ H(E)|ƒ is starlike univalent on E}

TR = {ƒ ∈ H(E)|ƒ is typically real on E}.

The uniform norm on (— 1, 1) of a function ƒ ∈ H(E) is defined by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 4 , 01 August 1989 , pp. 642 - 658
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Avriel, M., Nonlinear programming: Analysis and methods (Prentice Hall, Engelwood Cliffs, 1976).Google Scholar
2. de Branges, L., A proof of the Bieberbach conjecture, ACTA Math. 154 (1985), 137–152.Google Scholar
3. Duren, P. L., Univalent functions (Springer- Verlag, New York, 1983).Google Scholar
4. Rahman, Q. I. and St. Ruscheweyh, Markov's inequality for typically real polynomials, to appear in Journal of Mathematical Analysis and Applications.Google Scholar