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On uniformly convex functions

A. W. Goodman (1991)

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 defined by a purely geometric property. We obtain a few theorems about this new class and we point out a number of open problems.

On univalence of an integral operator

Szymon Ignaciuk (2009)

Annales UMCS, Mathematica

We consider the problem of univalence of the integral operator [...] Imposing on functions f(z), g(z) various conditions and making use of a close-to-convexity property of the operator, we establish many suffcient conditions for univalence. Our results extend earlier ones. Some questions remain open.

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