Sufficient conditions for starlike and convex functions

S. Ponnusamy, and P. Vasundhra. "Sufficient conditions for starlike and convex functions." Annales Polonici Mathematici 90.3 (2007): 277-288. <http://eudml.org/doc/280608>.

@article{S2007,
abstract = {For n ≥ 1, let denote the class of all analytic functions f in the unit disk Δ of the form $f(z) = z + ∑_\{k=2\}^∞ a_kz^k$. For Re α < 2 and γ > 0 given, let (γ,α) denote the class of all functions f ∈ satisfying the condition |f’(z) - α f(z)/z + α - 1| ≤ γ, z ∈ Δ. We find sufficient conditions for functions in (γ,α) to be starlike of order β. A generalization of this result along with some convolution results is also obtained.},
author = {S. Ponnusamy, P. Vasundhra},
journal = {Annales Polonici Mathematici},
keywords = {starlike function; Alexander transform; Bernardi operator},
language = {eng},
number = {3},
pages = {277-288},
title = {Sufficient conditions for starlike and convex functions},
url = {http://eudml.org/doc/280608},
volume = {90},
year = {2007},
}

TY - JOUR
AU - S. Ponnusamy
AU - P. Vasundhra
TI - Sufficient conditions for starlike and convex functions
JO - Annales Polonici Mathematici
PY - 2007
VL - 90
IS - 3
SP - 277
EP - 288
AB - For n ≥ 1, let denote the class of all analytic functions f in the unit disk Δ of the form $f(z) = z + ∑_{k=2}^∞ a_kz^k$. For Re α < 2 and γ > 0 given, let (γ,α) denote the class of all functions f ∈ satisfying the condition |f’(z) - α f(z)/z + α - 1| ≤ γ, z ∈ Δ. We find sufficient conditions for functions in (γ,α) to be starlike of order β. A generalization of this result along with some convolution results is also obtained.
LA - eng
KW - starlike function; Alexander transform; Bernardi operator
UR - http://eudml.org/doc/280608
ER -