Constants and Characterization for Certain Classes of Univalent Harmonic Mappings
Constants and Characterization for Certain Classes of Univalent Harmonic Mappings
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DOI：
10.1007/s00009-014-0443-9
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发表时间：
2015-07
影响因子：
1.1
通讯作者：
S. Ponnusamy;A. Kaliraj
中科院分区：
文献类型：
--
作者：
S. Ponnusamy;A. Kaliraj
本文得到了单位圆盘上某些保意义单叶调和函数族的增长性、覆盖性和面积定理。我们给出了我们为学习所考虑的类的积分表示。当第二次复伸缩为解析函数的平方时，还给出了与这类相关的极小曲面的表示。给出了保意义调和函数单叶逼近凸的一个一般充分条件。最后，我们研究了某些调和函数的单叶性和接近凸性的圆盘。
In this paper, we obtain growth, covering, and area theorems for certain families of sense preserving univalent harmonic functions which are close-to-convex in the unit disk. We present integral representation for the class that we have considered for our study. Representation of minimal surface associated with this class is also given whenever the second complex dilatation is a square of an analytic function. Also, we determine a general sufficient condition for a sense preserving harmonic function to be univalent and close-to-convex in. Finally, we examine the disk of univalency and close-to-convexity of certain classes of harmonic functions.