Directional convexity of normalized harmonic convex mappings. (English) Zbl 1482.31006
Summary: In this paper, we prove that convolution of two half-plane harmonic mappings with suitable dilatation is convex in some particular direction. We also prove that convolution of slanted half-plane mappings and slanted strip mapping with fixed dilatation is convex in a particular direction. We give some examples for support of our results.
MSC:
| 31A05 | Harmonic, subharmonic, superharmonic functions in two dimensions |
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
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