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On Convolution and Convex Combination of Harmonic Mappings
Journal of Mathematics
In this paper, the subclass of harmonic univalent functions by shearing construction is studied and this subclass of harmonic mappings needs a necessary and adequate condition to be convex in the horizontal direction. Furthermore, convolutions of two special subclasses of univalent harmonic mappings are shown to be convex in the horizontal direction. Also, the family of univalent harmonic mappings of the unit disk onto a region convex in the direction of the imaginary axis is introduced.doi:10.1155/2021/6553600 fatcat:r6wu4ncdwvcobonisujyhuqqde