Univalence, strong starlikeness and integral transforms

M. Obradović, S. Ponnusamy, and P. Vasundhra. "Univalence, strong starlikeness and integral transforms." Annales Polonici Mathematici 86.1 (2005): 1-13. <http://eudml.org/doc/280804>.

@article{M2005,
abstract = {Let represent the class of all normalized analytic functions f in the unit disc Δ. In the present work, we first obtain a necessary condition for convex functions in Δ. Conditions are established for a certain combination of functions to be starlike or convex in Δ. Also, using the Hadamard product as a tool, we obtain sufficient conditions for functions to be in the class of functions whose real part is positive. Moreover, we derive conditions on f and μ so that the non-linear integral transform $∫_0^z (ζ/f(ζ))^\{μ\} dζ$ is univalent in Δ. Finally, we give sufficient conditions for functions to be strongly starlike of order α.},
author = {M. Obradović, S. Ponnusamy, P. Vasundhra},
journal = {Annales Polonici Mathematici},
keywords = {univalent functions; starlike functions; strongly starlike functions; convex functions; Hadamard product; Gaussian hypergeometric series},
language = {eng},
number = {1},
pages = {1-13},
title = {Univalence, strong starlikeness and integral transforms},
url = {http://eudml.org/doc/280804},
volume = {86},
year = {2005},
}

TY - JOUR
AU - M. Obradović
AU - S. Ponnusamy
AU - P. Vasundhra
TI - Univalence, strong starlikeness and integral transforms
JO - Annales Polonici Mathematici
PY - 2005
VL - 86
IS - 1
SP - 1
EP - 13
AB - Let represent the class of all normalized analytic functions f in the unit disc Δ. In the present work, we first obtain a necessary condition for convex functions in Δ. Conditions are established for a certain combination of functions to be starlike or convex in Δ. Also, using the Hadamard product as a tool, we obtain sufficient conditions for functions to be in the class of functions whose real part is positive. Moreover, we derive conditions on f and μ so that the non-linear integral transform $∫_0^z (ζ/f(ζ))^{μ} dζ$ is univalent in Δ. Finally, we give sufficient conditions for functions to be strongly starlike of order α.
LA - eng
KW - univalent functions; starlike functions; strongly starlike functions; convex functions; Hadamard product; Gaussian hypergeometric series
UR - http://eudml.org/doc/280804
ER -