Rotations and convolutions of harmonic convex mappings

27 Sep 2019 · Li Liulan, Ponnusamy Saminathan ·

In this paper, we consider the convolutions of slanted half-plane mappings and strip mappings and generalize related results in general settings. We also consider a class of harmonic mappings containing slanted half-plane mappings and strip mappings and, as a consequence, we prove that the convex combination of such mappings is convex.