Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900347 | Journal of Mathematical Analysis and Applications | 2018 | 21 Pages |
Abstract
We study locally univalent functions f analytic in the unit disc D of the complex plane such that |fâ³(z)/fâ²(z)|(1â|z|2)â¤1+C(1â|z|) holds for all zâD, for some Câ(0,â). If Câ¤1, then f is univalent by Becker's univalence criterion. We discover that for Câ(1,â) the function f remains to be univalent in certain horodiscs. Sufficient conditions which imply that f is bounded, belongs to the Bloch space or belongs to the class of normal functions, are discussed. Moreover, we consider generalizations for locally univalent harmonic functions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Juha-Matti Huusko, Toni Vesikko,