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On the Residuum of Concave Univalent Functions

Wirths, K.-J. (2006)

Serdica Mathematical Journal

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 these functions is denoted...

On the univalent, bounded, non-vanishing and symmetric functions in the unit disk

J. Śladkowska (1996)

Annales Polonici Mathematici

The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

Kiryakova, Virginia (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, two operators introduced...

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