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

Sumit Nagpal;  V. Ravichandran — 2012

Annales Polonici Mathematici

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.

Fully starlike and fully convex harmonic mappings of order α

Sumit Nagpal;  V. Ravichandran — 2013

Annales Polonici Mathematici

The hereditary properties of convexity and starlikeness for conformal mappings do not generalize to univalent harmonic mappings. This failure leads to the notions of fully starlike and fully convex mappings. In this paper, properties of fully starlike mappings of order α and fully convex mappings of order α (0 ≤ α < 1) are studied; in particular, the bounds for the radius of full starlikeness of order α as well as the radius of full convexity of order α are determined for certain families of...

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