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A variational method for univalent functions connected with antigraphy

Janina Macura (1996)

Banach Center Publications

The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy e i φ ω ¯ + i ρ e i φ / 2 . Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.

Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions

Kanas, Stanislawa (1999)

Serdica Mathematical Journal

In this paper an alternative characterization of the class of functions called k -uniformly convex is found. Various relations concerning connections with other classes of univalent functions are given. Moreover a new class of univalent functions, analogous to the ’Mocanu class’ of functions, is introduced. Some results concerning this class are derived.

An Application of Convolution Integral

Nishiwaki, Junichi, Owa, Shigeyoshi (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 30C45Applying the Bernardi integral operator, an interesting convolution integral is introduced. The object of the present paper is to derive some convolution integral properties of functions f(z) to be in the subclasses of the classes S*(α) and Κ(α) by making use of their coefficient inequalities.

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