Journal ArticleDOI
Aharonov invariants and univalent functions
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Several properties of a certain series of differential operators which are invariant under the Mobius group (Aharonov invariants) are proved, and in terms of this series new conditions for univalence and quasiconformal extendability of meromorphic functions are established as discussed by the authors.Abstract:
Several properties of a certain series of differential operators which are invariant under the Mobius group (Aharonov invariants) are proved, and in terms of this series new conditions for univalence and quasiconformal extendability of meromorphic functions are established.read more
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Distortion theorems for higher order Schwarzian derivatives of univalent functions
TL;DR: In this paper, a simple differential equation for the Loewner flow of the Schwarzian derivative of a given function f ∈ S is derived, which is used to prove bounds on higher order Schwarzian derivatives which are sharp for the Koebe function.
Journal ArticleDOI
Sharp coefficient bounds for starlike functions associated with the Bell numbers
TL;DR: In this paper, the first three consecutive higher-order Schwarzian derivatives for functions in the class SB∗ $\\begin{array}{} \\mathcal{S}^*_B \\end{array}$ are investigated.
Journal ArticleDOI
Invariant Schwarzian Derivatives of Higher Order
Seong A. Kim,Toshiyuki Sugawa +1 more
TL;DR: In this article, the authors derive relations between the Aharonov invariants and Tamanoi's Schwarzian derivatives of higher order and give a recursive formula for the invariant Schwarzians of a holomorphic map between Riemann surfaces with conformal metrics.
Journal ArticleDOI
Sufficient conditions for the finite-valence of analytic functions and their applications
TL;DR: A survey of sufficient univalence and p-valence conditions for analytic and meromorphic functions of a complex variable is given in this article, where a survey of the results on the conditions for the univalent solvability of applied inverse boundary value problems is given.
References
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Book
Advanced Combinatorics: The Art of Finite and Infinite Expansions
Louis Comtet,J. W. Nienhuys +1 more
TL;DR: A vocabulary of combinatorial analysis can be found in this paper, where the authors define definitions of partitions of an integer [n]- 22 Generating Functions of p(n) and P(n, m)- 23 Conditional Partitions- 24 Ferrers Diagrams- 25 Special Identities 'Formal' and 'Combinatorial' Proofs- 26 Partitions with Forbidden Summands Denumerants- Supplement and Exercises- III Identities and Expansions- III Identity and Expansion of a Product of Sums Abel Identity- 31
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Riemann's mapping theorem for variable metrics*
Lars V. Ahlfors,Lipman Bers +1 more
Journal ArticleDOI
Representation of functions by matrices. application to faber polynomials
TL;DR: In this paper, it was shown that one row of the matrix is sufficient to define the function so that the whole matrix furnishes a superabundance of information about the function.
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A necessary and sufficient condition for univalence of a meromorphic function
Journal ArticleDOI
Explicit formulas for the coefficients of Faber polynomials with respect to univalent functions of the class Σ
TL;DR: In this paper, the coefficients of the Faber polynomials with respect to univalent functions of the class S were given explicit formulas for functions in l. The method used in this paper is different from the one that was used to obtain explicit expressions for the Grunsky coefficients for functions of S (6).