On the Existence of Functions being Univalent in Half-plane together with their Derivatives
Articles
J. Kirjackis
Vilnius Gediminas Technical University, Lithuania
Published 2001-12-05
https://doi.org/10.15388/NA.2001.6.1.15214
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Keywords

class of univalent functions
unit disc
half-plane
existence

How to Cite

Kirjackis, J. (2001) “On the Existence of Functions being Univalent in Half-plane together with their Derivatives”, Nonlinear Analysis: Modelling and Control, 6(2), pp. 43–50. doi:10.15388/NA.2001.6.1.15214.

Abstract

In articles [1]-[3] a class of functions being univalent in unit disc with all their derivatives was investigated. It was proved such functions exist and must be the entire functions of exponential type. The example of such a function is an exponential function f(z) = ez. In this work the question on existence of functions, beeing univalent in half-plane with all their derivatives was raised and the negative answer to such question was given.

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