L�wnersche Differentialgleichung und Schlichtheitskriterien

Becker, Jochen

doi:10.1007/bf01433462

Cited by 45 publications

(20 citation statements)

References 8 publications

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“…The case s = 1 is due to J. Becker [3]. Theorem 2 has an interesting limiting case which can be shown to represent a univalence condition too 1 : b Corollary 2.…”

Section: Ze A' Then F Is Univalent In A'mentioning

confidence: 99%

An extension of Becker's univalence condition

Ruscheweyh

1976

Math. Ann.

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“…The case s = 1 is due to J. Becker [3]. Theorem 2 has an interesting limiting case which can be shown to represent a univalence condition too 1 : b Corollary 2.…”

Section: Ze A' Then F Is Univalent In A'mentioning

confidence: 99%

An extension of Becker's univalence condition

Ruscheweyh

1976

Math. Ann.

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“…Becker ( [3,4]; see also [5]) studied the general form of solutions to the Loewner differential equation in one complex variable, i.e.…”

Section: Introductionmentioning

confidence: 99%

Solutions for the generalized Loewner differential equation in several complex variables

et al. 2009

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We generalize a one-variable result of J. Becker to several complex variables. We determine the form of arbitrary solutions of the Loewner differential equation that is satisfied by univalent subordination chains of the form(The notion of parametric representation has a useful generalization under these conditions, so that one has a canonical solution of the Loewner differential equation.) In particular, we determine the form of the univalent solutions. The results are applied to subordination chains generated by spirallike mappings on the unit ball in C n . Finally, we determine the form of the solutions in the presence of certain coefficient bounds. I.

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“…For f (ζ) = g(ζ), h(ζ) = 1 and α = 1 2 in Theorem 3.1 we obtain well-known Becker's univalence criterion [1] in U * . is satisfied for all ζ ∈ U * , then f is univalent in U * .…”

Section: From (32)-(34) It Follows In Particular Thatmentioning

confidence: 63%

“…Two of the most important and known univalence criteria for analytic functions defined in U * were obtained by Becker [1] and Nehari [8]. Some extensions of these two criteria were given by Lewandowski [5], [6] and Ruscheweyh [11].…”

Section: Introductionmentioning

confidence: 99%