Some subclasses of close-to-convex functions

@article{AdamLecko1993,
abstract = {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 $Re\{e^\{iβ\}(1 - α²z²)f^\{\prime \}(z)\} < 0$ for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in $C_β(α)$ are examined.},
author = {Adam Lecko},
journal = {Annales Polonici Mathematici},
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; distortion theorems},
language = {eng},
number = {1},
pages = {53-64},
title = {Some subclasses of close-to-convex functions},
url = {http://eudml.org/doc/262387},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Adam Lecko
TI - Some subclasses of close-to-convex functions
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 1
SP - 53
EP - 64
AB - 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 $Re{e^{iβ}(1 - α²z²)f^{\prime }(z)} < 0$ for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in $C_β(α)$ are examined.
LA - eng
KW - 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; distortion theorems
UR - http://eudml.org/doc/262387
ER -