Functions of bounded boundary rotation

Bernard Pinchuk

Research output: Contribution to journalArticlepeer-review

149 Scopus citations


Classes of functions U k, which generalize starlike functions in the same manner that the class V k of functions with boundary rotation bounded by kπ generalizes convex functions, are defined. The radius of univalence and starlikeness is determined. The behavior of f α(z) = ∫ 0 z [f'(t)]α dt is determined for various classes of functions. It is shown that the image of |z|<1 under V kfunctions contains the disc of radius 1/k centered at the origin, and V k functions are continuous in |z|≦1 with the exception of at most [k/2+1] points on |z|=1.

Original languageEnglish
Pages (from-to)6-16
Number of pages11
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Mar 1971
Externally publishedYes


Dive into the research topics of 'Functions of bounded boundary rotation'. Together they form a unique fingerprint.

Cite this