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Details van artikel 38 van 269 gevonden artikelen
| Titel: |
Communicatded by real analogues of pre-schwarzian univalence criteria |
| Auteur: |
Chuaqui, M. Gevirtz, J. |
| Verschenen in: |
Complex variables and elliptic equations |
| Paginering: | Jaargang 42 (2000) nr. 1 pagina's 41-56 |
| Jaar: |
2000-07 |
| Inhoud: |
Let [image omitted] (the pre-Schwarzian) and [image omitted] (the Schwarzian). Because extremal behavior for Nehari's celebrated sharp univalence criteria of the form [image omitted] in the unit disc D is manifested by functions which display extremal behavior for the corresponding univalence criteria for [image omitted] , one is led to ask whether the same holds for the pre-Schwarzian analogues[image omitted] , and in particular, for the longstanding open question as to the largest constant c for which [image omitted] implies univalence in D. For a wide class of functions p we apply a sequence of variational arguments to obtain a characterization of the largest cp for which [image omitted] on (-1, 1) implies that f is one-to-one as the first eigenvalue of a certain nonlinear boundary value problem of Sturm-Liouville type. Using this we show that for no such p is extremal behavior for a univalence criterion [image omitted] manifested by an extremal function for a corresponding real criterion. In addition, we show that when [image omitted] is replaced by [image omitted] the numerically sharp real univalence criteria obtained extend, with the same constants, to mappings of the interval into [image omitted] |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 38 van 269 gevonden artikelen
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