一类近于凸调和映照的凸像半径与Pre-Schwarz导数的估计

Abstract

Abstract:

In this paper, the following subclass of H
P⁰(α)={f=h+g∈H:Re{h'(z)-α}>|g'(z)|, z∈D and g'(0)=0}
is studied, where α∈[0,1) and H is the class of all normalized sense preserving harmonic mappings defined in the unit disk D. Estimations of the convexity and starlike radii of P⁰(α) are given, which improve the relative results in[8, 9]. A distortion theorem and a lower bound of |f(D)| for all f∈P⁰(α) are obtained. The upper bound of Pre-Schwarzian norms of functions in a subclass of SHU containing P⁰(α) is estimated and the quasiconformality is discussed also.

Key words: Close to convex functions, Convexity and starlike radii, Distortion theorem, Quasiconformal mapping, Pre-Schwarz derivative

CLC Number:

O174.55

Qi Yi, Shi Qingtian. Estimations of Convexity Radius and the Norm of Pre-Schwarz Derivative for Close to Convex Harmonic Mappings[J].Acta mathematica scientia,Series A, 2016, 36(6): 1057-1066.

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References

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Estimations of Convexity Radius and the Norm of Pre-Schwarz Derivative for Close to Convex Harmonic Mappings

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