On Uniformly Starlike Functions
نویسنده
چکیده
These are normalized functions regular and univalent in E: IzI < 1, for which f( E) is starlike with respect to the origin. Let y be a circle contained in E and let [ be the center of y. The Pinchuk question is this: Iff(z) is in ST, is it true thatf(y) is a closed curve that is starlike with respect tof(i)? In Section 5 we will see that the answer is no. There seems to be no reason to demand that the complete circle y lies in E, and we replace this condition with the stronger condition that y is an arc of a circle contained in E, but we still ask that [ the center of y is also in E. Thus we have,
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