On Fully-Convex harmonic functions and their extension
Keywords:
Uniformly convex function, Fully-Convex function, Harmonic function, Convolution
Abstract
Uniformly convex univalent functions that introduced by Goodman, maps every circular arc contained in the open unit disk with center in it into a convex curve. On the other hand, a fully-convex harmonic function, maps each subdisk $|z|=r<1$ onto a convex curve. Here we synthesis these two ideas and introduce a family of univalent harmonic functions which are fully-convex and uniformly convex also. In the following we will mention some examples of this subclass and obtain a necessary and sufficient conditions and finally a coefficient condition will attain with convolution.Downloads
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Published
2018-02-19
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Section
Research Articles
Copyright (c) 2018 Boletim da Sociedade Paranaense de Matemática
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