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Displaying similar documents to “On a subclass of univalent functions II”

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.

On the class of functions strongly starlike of order α with respect to a point

Adam Lecko (1998)

Annales Polonici Mathematici

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We consider the class 𝓩(k;w), k ∈ [0,2], w ∈ ℂ, of plane domains Ω called k-starlike with respect to the point w. An analytic characterization of regular and univalent functions f such that f(U) is in 𝓩(k;w), where w ∈ f(U), is presented. In particular, for k = 0 we obtain the well known analytic condition for a function f to be starlike w.r.t. w, i.e. to be regular and univalent in U and have f(U) starlike w.r.t. w ∈ f(U).