Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T09:39:50.787Z Has data issue: false hasContentIssue false
  • English
  • Français

On the class of functions convex in the negative direction of the imaginary axis

Published online by Cambridge University Press:  09 April 2009

Adam Lecko
Adam Lecko
Affiliation:
Department of Mathematics Technical University of Rzeszówul. W. Pola 2, 35-959 Rzeszów, Poland e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we present a new proof of the equivalence of the analytic and the geometric characterization of the class of functions convex in the negative or positive direction of the imaginary axis.

Keywords

functions convex in the negative direction of the imaginary axisgeometric characterizationJulia Lemma
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 1 , August 2002 , pp. 1 - 10
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Carathéodory, C., Conformal representation (Cambridge University Press, Cambridge, 1963).Google Scholar
[2]Ciozda, W., ‘Sur la classe des fonctions convexes vers l'axe réel négatif’, Bull. Acad. Polon. Sci. 27 (1979), 225–261.Google Scholar
[3]Hengartner, W. and Schober, G., ‘On schlicht mappings to domains convex in one direction’, Comment. Math. Helv. 45 (1970), 303–314.CrossRefGoogle Scholar
[4]Julia, G., ‘Extension nouvelle d'un lemme de Schwarz’, Acta Math. 42 (1918), 349–355.CrossRefGoogle Scholar
[5]Kaplan, W., ‘Close-to-convex schlicht functions’, Mich. Math. J. 1 (1952), 169–185.CrossRefGoogle Scholar
[6]Pommerenke, Ch., Boundary behaviour of conformal maps (Springer, Berlin, 1992).CrossRefGoogle Scholar
[7]Robertson, M. S., ‘Analytic functions star-like in one direction’, Amer. J. Math. 58 (1936), 465–472.CrossRefGoogle Scholar
[8]Royster, W. and Ziegler, M., ‘Univalent functions convex in one direction’, Publ. Math. Debrecen 23 (1976), 339–345.CrossRefGoogle Scholar