On the DCP property of exponential partial sums
In [6] we proved that the functions [GRAPHICS] are convex univalent in the unit disk D, which extended previous results of Suffridge [8]. In the present paper we prove a conjecture made in [6], namely, that the functions (*), under the further restriction that 0 not equal a(1) = a(2), even belong to the much narrower class DCP of the functions which, under Hadamard product, preserve direction-convexity of univalent functions in the unit disk D.
dcp hadamard product univalent functions direction-convexity-preserving-functions computer algebra