In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.
@article{bwmeta1.element.bwnjournal-article-apmv61z2p135bwm,
author = {Rosihan M. Ali and S. Ponnusamy and Vikramaditya Singh},
title = {Starlikeness of functions satisfying a differential inequality},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {135-140},
zbl = {0818.30006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv61z2p135bwm}
}
Rosihan M. Ali; S. Ponnusamy; Vikramaditya Singh. Starlikeness of functions satisfying a differential inequality. Annales Polonici Mathematici, Tome 62 (1995) pp. 135-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv61z2p135bwm/
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