On uniformly convex functions

  title={On uniformly convex functions},
  author={A. W. Goodman},
  journal={Annales Polonici Mathematici},
  • A. Goodman
  • Published 1991
  • Mathematics
  • Annales Polonici Mathematici
We introduce a new class of normalized functions regular and univalent in the unit disk. These functions, called uniformly convex functions, are dened by a purely geometric property. We obtain a few theorems about this new class and we point out a number of open problems. 

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The two examples z+ (1 +e)z2/2 and z+(1 +e)z2/4 with e>0, show that the right sides of (2) and (3) cannot be increased without destroying respectively the starlikeness and convexity of the image

Vandenhoeck & Ruprecht

  • Göttingen
  • 1975

Goluz in, On the majorization principle in function theory

  • Dokl. Akad. Nauk SSSR
  • 1935