Univalent functions. Selected topics

DOI10.1007/BFb0077279zbMath0306.30018OpenAlexW4206344085MaRDI QIDQ1217914

Glenn Schober

Publication date: 1975

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bfb0077279

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Extremal problems for conformal and quasiconformal mappings, variational methods (30C70) Quasiconformal mappings in the complex plane (30C62) Extremal problems for conformal and quasiconformal mappings, other methods (30C75) General theory of univalent and multivalent functions of one complex variable (30C55) Coefficient problems for univalent and multivalent functions of one complex variable (30C50)

Related Items

Continuous affine functionals on convex families of analytic functions ⋮ On nonvanishing univalent functions with real coefficients ⋮ On coefficients problems for typically real functions related to Gegenbauer polynomials ⋮ Hermitian Forms in Function Theory ⋮ Punishing factors for angles ⋮ On the structure of support points in the class \(\Sigma\) ⋮ Coefficients of Inverses of Meromorphic Univalent Functions ⋮ Coefficient bounds for analytic functions in an ellipse ⋮ Remarks on geometric properties of certain coefficient estimates ⋮ Geometric Properties of a Class of Support Points of Univalent Functions ⋮ On the Schwarzian coefficients of univalent functions ⋮ Numerical conformal mapping methods based on Faber series ⋮ Starlike cases of the generalized Goodman conjecture ⋮ Generalizastions of coefficients estimates for certain classes of analytic functions ⋮ A variational method for general families of quasiconformal mappings ⋮ General distortion theorem for univalent functions with quasiconformal extension ⋮ Coefficients of inverses of univalent functions with quasiconformal extensions ⋮ On convolution and \(q\)-calculus ⋮ Logarithmic coefficients of univalent functions ⋮ Some convexity and convolution theorems for analytic functions ⋮ Einige Bemerkungen zu Flächensätzen für quasikonform fortsetzbare Abbildungen ⋮ Covering numbers and schlicht functions ⋮ Majorization problem for certain class of \(p\)-valently analytic function defined by generalized fractional differintegral operator ⋮ The dielectric Green's function and quasiconformal mapping ⋮ Some extremal problems for functions of bounded boundary rotation ⋮ Support Points of Families of Analytic Functions Described by Subordination ⋮ On the Faber coefficients of functions univalent in an ellipse ⋮ Derivatives of close-to-convex functions, integral means and bounded mean oscillation ⋮ Unnamed Item ⋮ Some properties of two subclasses of \(k\)-fold symmetric functions associated with Srivastava-Attiya operator ⋮ Sufficient conditions for the finite-valence of analytic functions and their applications ⋮ The punishing factors for convex pairs are \(2^{n-1}\) ⋮ Loewner Theory for Quasiconformal Extensions: Old and New ⋮ Extreme harmonic functions on a ball ⋮ The simple-zero conjecture for support points in Σ ⋮ On the second variation for univalent functions ⋮ Extreme and support points of the class of non-vanishing univalent functions ⋮ Univalent functions with quasiconformal extensions: Becker’s class and estimates of the third coefficient ⋮ The boundary behavior of conformal mappings with quasiconformal extensions ⋮ Coefficients of Symmetric Functions of Bounded Boundary Rotation ⋮ Large linear manifolds of noncontinuable boundary-regular holomorphic functions ⋮ Chordal Loewner chains with quasiconformal extensions ⋮ On Coefficient Inequalities for Meromorphic Univalent Functions ⋮ Quasiconformal extensions, Loewner chains, and the \(\lambda \)-lemma ⋮ Hyperbolic metrics on universal Teichmüller space and extremal problems ⋮ A survey with open problems on univalent functions whose coefficients are negative ⋮ Analytic functions of a proper contraction ⋮ Analytic functions of a proper contraction ⋮ Solutions with singularities of a certain equation of mathematical physics ⋮ Berechnung einer quasikonformen Extremalfunktion ⋮ Über einige Extremalprobleme der konformen Abbildung ⋮ The conformal radius as a function and its gradient image ⋮ On univalent functions with quasiconformal extensions over the boundary ⋮ Coefficients of univalent functions ⋮ Nonvanishing Meromorphic Univalent Functions ⋮ Asymptotische Koeffizientenabschätzungen für die quasikonform fortsetzbaren Abbildungen der Klasse S bzw. Σ ⋮ Complex geodesics and variational calculus for univalent functions ⋮ A Coefficient Problem with Typically Real Extremal Function ⋮ Die Koeffizientenbedingungen vom GRUNSKYschen Typ für quasikonforme Abbildungen mit längs zweier Kreise springender Dilatationsschranke ⋮ Lagrange multipliers in variational methods for univalent functions ⋮ Univalent Functions and the Pompeiu Problem ⋮ Extremal problems for Fredholm eigenvalues ⋮ Extremal functions for functionals on some classes of analytic functions ⋮ Über die quasikonforme Fortsetzung schlichter Funktionen ⋮ Some results on convex meromorphic functions ⋮ Majorizations and quasi-subordinations for certain analytic functions ⋮ Nonvanishing univalent functions ⋮ Compact deformations of Fuchsian groups ⋮ Support points of families of starlike mappings ⋮ Properties of associated quadratic differentials in certain extremal problems ⋮ Extreme points and minimal outer area problem for meromorphic univalent functions ⋮ A certain subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials ⋮ On sets of range uniqueness ⋮ Hornich operations on functions of bounded boundary rotations and order \(\alpha\) ⋮ Bounds for the Faber coefficients of certain classes of functions analytic in an ellipse ⋮ Faber polynomials with applications to univalent functions with quasiconformal extensions ⋮ A Method for Investigating Geometric Properties of Support Points and Applications ⋮ Closed convex hull of the family of multivalently close-to-convex functions of order \(\beta\) ⋮ Classical families of univalent functions in the Hornich space ⋮ A proof of the Bieberbach conjecture ⋮ On the univalency of regular functions ⋮ Coefficient bounds for starlike and close-to-convex functions in an ellipse ⋮ Analytic eigendistributions and applications to homogeneous trees.