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Starlike Univalent Functions Bounded on the Real Axis
Published online by Cambridge University Press: 20 November 2018
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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
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- Copyright © Canadian Mathematical Society 1989
References
1.
Avriel, M., Nonlinear programming: Analysis and methods (Prentice Hall, Engelwood Cliffs, 1976).Google Scholar
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de Branges, L., A proof of the Bieberbach conjecture,
ACTA Math.
154 (1985), 137–152.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
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