Geodesic
Some subclasses of close-to-convex functions
Annales Polonici Mathematici, Tome 58 (1993) no. 1, pp. 53-64.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes $C_β(α)$ defined as follows: a function f regular in U = {z: |z| 1} of the form $f(z) = z + ∑_{n=1}^{∞} a_n z^n$, z ∈ U, belongs to the class $C_β(α)$ if $Re{e^{iβ}(1 - α²z²)f'(z)} 0$ for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in $C_β(α)$ are examined.
DOI : 10.4064/ap-58-1-53-64
Keywords: close-to-convex functions, close-to-convex functions with argument β, functions convex in the direction of the imaginary axis, functions of bounded rotation with argument β

Adam Lecko 1

1 
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Adam Lecko. Some subclasses of close-to-convex functions. Annales Polonici Mathematici, Tome 58 (1993) no. 1, pp. 53-64. doi : 10.4064/ap-58-1-53-64. http://geodesic.mathdoc.fr/articles/10.4064/ap-58-1-53-64/

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