Abstract
Classes of functionsU k, which generalize starlike functions in the same manner that the classV k of functions with boundary rotation bounded bykπ generalizes convex functions, are defined. The radius of univalence and starlikeness is determined. The behavior off α(z) = ∫ z0 [f'(t)]α dt is determined for various classes of functions. It is shown that the image of |z|<1 underV kfunctions contains the disc of radius 1/k centered at the origin, andV k functions are continuous in |z|≦1 with the exception of at most [k/2+1] points on |z|=1.
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Pinchuk, B. Functions of bounded boundary rotation. Israel J. Math. 10, 6–16 (1971). https://doi.org/10.1007/BF02771515
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DOI: https://doi.org/10.1007/BF02771515