Displaying similar documents to “Concave schlicht functions with bounded opening angle at infinity.”

On the Residuum of Concave Univalent Functions

Wirths, K.-J. (2006)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 30C25, 30C45. Let D denote the open unit disc and f:D→[`C] be meromorphic and injective in D. We further assume that f has a simple pole at the point p О (0,1) and is normalized by f(0) = 0 and f′(0) = 1. In particular, we are concerned with f that map D onto a domain whose complement with respect to [`C] is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of...

Applications of the theory of differential subordination for functions with fixed initial coefficient to univalent functions

Sumit Nagpal, V. Ravichandran (2012)

Annales Polonici Mathematici

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By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions becomes evident in the results obtained.