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Israel Journal of Mathematics

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

Functions of bounded boundary rotation

  • Bernard Pinchuk
Article

Abstract

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.

Keywords

Univalent Function Positive Real Part Closed Disc Michigan Math Large Disc 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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