Israel Journal of Mathematics

, Volume 10, Issue 1, pp 6–16 | Cite as

Functions of bounded boundary rotation

  • Bernard Pinchuk


Classes of functionsU k, which generalize starlike functions in the same manner that the classV k of functions with boundary rotation bounded by generalizes convex functions, are defined. The radius of univalence and starlikeness is determined. The behavior off α(z) = ∫ 0 z [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.


Univalent Function Positive Real Part Closed Disc Michigan Math Large Disc 
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Copyright information

© The Weizmann Science Press of Israel 1971

Authors and Affiliations

  • Bernard Pinchuk
    • 1
  1. 1.The Hebrew University of JerusalemIsrael

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