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 is univalent in Δ. Finally, we give sufficient conditions for functions to be strongly starlike of order α.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-1,
author = {M. Obradovi\'c and S. Ponnusamy and P. Vasundhra},
title = {Univalence, strong starlikeness and integral transforms},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {1-13},
zbl = {1084.30014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-1}
}
M. Obradović; S. Ponnusamy; P. Vasundhra. Univalence, strong starlikeness and integral transforms. Annales Polonici Mathematici, Tome 85 (2005) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-1-1/