Convolutions of planar harmonic convex mappings
Convolutions of planar harmonic convex mappings
复制标题
DOI：
10.1080/17476930108815381
复制
发表时间：
2001-09
期刊：
影响因子：
--
通讯作者：
M. Dorff
中科院分区：
文献类型：
--
作者：
M. Dorff
Ruscheweyh和Sheil-Small证明了K中单叶解析映射的卷积保持凸性，但当我们考虑K中单叶调和凸映射的卷积时，这一性质就不成立了。事实上，这样的卷积可能不是单价的。建立了关于单叶调和凸映射卷积的一些结果，只要它是局部单叶的。特别地，我们证明了右半平面映射与另一个右半平面映射或垂直条形映射在实轴方向上的卷积是凸的。此外，我们还给出了垂直条形映射的卷积在实轴方向上凸的一个条件
Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convex mappings in , this property does not hold. In fact, such convolutions may not be univalent. We establish some results concerning the convolution of univalent harmonic convex mappings provided that it is locally univalent. In particular, we show that the convolution of a right half-plane mapping in with either another right half-plane mapping or a vertical strip mapping in is convex in the direction of the real axis. Further, we give a condition under which the convolution of a vertical strip mapping in with itself will be convex in the direction of the real axis