All α-Convex Functions are Univalent and Starlike

DOI10.2307/2039483zbMath0258.30012OpenAlexW4246303141MaRDI QIDQ5673688

Petru T. Mocanu, Maxwell O. Reade, Sanford S. Miller

Publication date: 1973

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2039483

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45)

Related Items (43)

On a class of \(\alpha\)-convex functions subordinate to a shell shaped region ⋮ Unnamed Item ⋮ Differential inequalities for certain analytic functions ⋮ Unnamed Item ⋮ Coefficient functionals for alpha-convex functions associated with the exponential function ⋮ On some subclasses of \(m\)-fold symmetric analytic functions ⋮ \(\alpha\)-convex functions for \(\alpha <0\) ⋮ Boundaries of \(\alpha\)-convexity for subclasses of starlike functions ⋮ Application of pythagorean means and differential subordination ⋮ The starlikeness of analytic functions of koebe type ⋮ On uniformly Bazilevic and related functions ⋮ Extremal properties of some spirallike functions ⋮ Certain conditions for starlikeness of analytic functions of Koebe type ⋮ alpha-convexity of order beta of the class of all regular univalent functions in a circle ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Sufficient conditions for the finite-valence of analytic functions and their applications ⋮ Estimates of initial coefficients for bi-univalent functions ⋮ Estimation for initial coefficients of bi-univalent λ-convex analytic functions in the unit disc ⋮ Bounds for the second Hankel determinant of certain bi-univalent functions ⋮ Unnamed Item ⋮ On some ``collateral effects in the alpha-convex theory ⋮ An upper bound to the second Hankel determinant for functions in Mocanu class ⋮ On analytic functions with generalized bounded Mocanu variation ⋮ A survey with open problems on univalent functions whose coefficients are negative ⋮ Some applications of Briot-Bouquet differential subordination ⋮ On some properties of schlicht functions ⋮ Some applications of differential subordination ⋮ Unnamed Item ⋮ Some applications of differential subordination ⋮ Some properties of the class \(\mathcal{U}\) ⋮ Some properties of starlike univalent functions ⋮ Coefficients of alpha-convex functions of order beta ⋮ On a Subclass of Spiral-Like Functions ⋮ The class of alpha-convex functions ⋮ Differential subordinations and Pythagorean means ⋮ Order of starlikeness for multipliers of univalent functions ⋮ Classes of functions whose derivatives have positive real part ⋮ On generalized gamma-Bazilevic functions ⋮ On analytic functions related with generalized Robertson functions ⋮ Notes on p-valently Bazilevich functions ⋮ New Subclasses of the Class of Close-to-Convex Functions ⋮ Majorization problems for a class of analytic functions defined by subordination

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