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1

On the geometrical properties of some classes of complex harmonic functions defined by analytic or coefficient conditions with complex parameter

Sibelska A.

Journal of Applied Analysis

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2014

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Vol. 20, nr 1

77--85

EN

In the paper there are determined, for some classes defined by coefficient or analytic conditions, the sets of complex parameter γ, for which all the functions of the appropriate family have some geometrical properties. There are also provided the examples of the mappings showing that some inclusions between classes are impossible or confirming that sets of the parameter γ cannot be extended in some cases without loss of these geometric properties.

2

On classes of meromorphic or complex harmonic functions with a pole at the infinity

Jakubowski Z., Sibelska A.

Demonstratio Mathematica

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2009

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Vol. 42, nr 3

479-489

EN

In this article we investigate some classes of meromorphic or complex harmonie functions with a pole, which are generated either by analytic conditions or by "coefficient inequalities". There are given theorems, which combine the geometrical properties of functions of the introduced classes. Some results broaden knowledge about the classes of functions, which were investigated in [15]. The main inspiration for the reaserch were the papers [4] and [11]. The part of results were presented in the XII-th International Mathematically-Informatical Conference in Chełm (2nd-5th July, 2006) [12].

3

On some coefficient conditions for complex harmonic mappings with a pole at the infinity

Sibelska A.

Demonstratio Mathematica

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2006

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Vol. 39, nr 2

335-346

EN

In 1984 J. Clunie and T. Sheil-Small initiated studies of complex functions harmonic in the unit disc. In 1987 W. Hergartner and G. Schober considered mappings of this type, defined in the domain U = {z is an element of C : \z\ > 1}. Several mathematicians examine classes of complex harmonic functions with some coefficient conditions, defined in the unit disc (e.g. [2], [5], [10], [1] [9]) or in U (e.g. [8], [7]). We investigate the classes of mappings harmonic in U with coefficient conditions more general than the considered in paper [8].