On the Zalcman conjecture for starlike and typically real functions

DOI10.1007/BF01162720zbMath0541.30004WikidataQ123118562 ScholiaQ123118562MaRDI QIDQ794793

Johnny E. Brown, Anna Tsao

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173688

zbMATH Keywords

starlike functionstypically real functionsBieberbach conjectureZalcman conjecture

Mathematics Subject Classification ID

Coefficient problems for univalent and multivalent functions of one complex variable (30C50)

Related Items (25)

On the generalized Zalcman functional $\lambda a_n^2-a_{2n-1}$ in the close-to-convex family ⋮ Unnamed Item ⋮ Univalent functions and holomorphic motions ⋮ Generalized Zalcman conjecture for convex functions of order \(\alpha\) ⋮ A generalization of Livingston's coefficient inequalities for functions with positive real part ⋮ Inequalities for the coefficients of Schwarz functions ⋮ An evolutionary approach to the coefficient problems in the class of starlike functions ⋮ The Zalcman conjecture for certain analytic and univalent functions ⋮ Coefficient estimates for starlike and convex functions related to sigmoid functions ⋮ Unnamed Item ⋮ On the Fekete-Szegö type functionals for functions which are convex in the direction of the imaginary axis ⋮ Sharp Fekete-Szegö coefficients functional, distortion and growth inequalities for certain $p$-valent close-to-convex functions ⋮ On coefficient functionals associated with the Zalcman conjecture ⋮ Extremal problems on the class of convex functions of order \(-1/2\) ⋮ Generalized Zalcman conjecture for some classes of analytic functions ⋮ Constrained coefficients problem for generalized typically real functions ⋮ Constrained coefficients problem for generalized typically real functions ⋮ Unnamed Item ⋮ The Zalcman Conjecture for Close-to-Convex Functions ⋮ Sharp bounds of Fekete-Szegő functional for quasi-subordination class ⋮ The sharp bounds of the second and third Hankel determinants for the class \(\mathcal{SL}^*\) ⋮ Fourth Hankel determinant for a subclass of starlike functions based on modified sigmoid ⋮ Hankel, Toeplitz, and Hermitian-Toeplitz determinants for certain close-to-convex functions ⋮ On estimates of some coefficient functionals for certain meromorphic univalent functions ⋮ Generalized Zalcman conjecture for starlike and typically real functions

Cites Work

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• Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen
• On normal and automorphic functions
• Quadratic inequalities and coefficient estimates for schlicht functions
• Coefficients of univalent functions
• The Coefficients of Multivalent Close-to-Convex Functions
• Convex Hulls of Some Classical Families of Univalent Functions

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