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A Variation of the Koebe Mapping in a Dense Subset of S

Published online by Cambridge University Press:  20 November 2018

D. Bshouty
Affiliation:
Technion, Haifa, Israel
W. Hengartner
Affiliation:
Université Laval, Québec, Québec
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Let H(U) be the linear space of holomorphic functions defined on the unit disk U endowed with the topology of normal (locally uniform) convergence. For a subset EH(U) we denote by Ē the closure of E with respect to the above topology. The topological dual space of H(U) is denoted by H′(U).

Let D, 0 ∊ D, be a simply connected domain in C. The unique univalent conformal mapping ϕ from U onto D, normalized by ϕ(0) = 0 and ϕ′(0) > 0 will be called “the Riemann Mapping onto D”. Let S be the set of all normalized univalent functions

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Bombieri, E., SulTintegrazione approssimata delVequazione differenziale di Loewner e le sue applicazioni alia theoria delle funzioni univalenti, Universita di Milano (1963).Google Scholar
2. Bombieri, E., On the local maximum property of the Koebe function, Invent. Math. 4, 2667 .Google Scholar
3. Duren, P. L. and Schiffer, M., The theory of the second variation in extremum problems for univalent functions, J. Anal. Math. 70(1962/63), 193252.Google Scholar
4. Ruscheweyh, S., Duality of Hadamard products with applications to extremal problems for functions regular in the unit disk, Trans. Amer. Math. Soc. 210 (1975), 6374.Google Scholar
5. Sheil-Small, T., The Hadamard product and linear transformations of classes of analytic functions, J. Anal. Math. 34 (1978), 204239.Google Scholar