We consider the class 𝓩(k;w), k ∈ [0,2], w ∈ ℂ, of plane domains Ω called k-starlike with respect to the point w. An analytic characterization of regular and univalent functions f such that f(U) is in 𝓩(k;w), where w ∈ f(U), is presented. In particular, for k = 0 we obtain the well known analytic condition for a function f to be starlike w.r.t. w, i.e. to be regular and univalent in U and have f(U) starlike w.r.t. w ∈ f(U).
@article{bwmeta1.element.bwnjournal-article-apmv68z2p107bwm,
author = {Adam Lecko},
title = {On the class of functions strongly starlike of order $\alpha$ with respect to a point},
journal = {Annales Polonici Mathematici},
volume = {69},
year = {1998},
pages = {107-117},
zbl = {0901.30017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv68z2p107bwm}
}
Adam Lecko. On the class of functions strongly starlike of order α with respect to a point. Annales Polonici Mathematici, Tome 69 (1998) pp. 107-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv68z2p107bwm/
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