Rotations and convolutions of harmonic convex mappings

Research paper by Liulan Li, Saminathan Ponnusamy

Indexed on: 07 Jan '21Published on: 27 Sep '19Published in: arXiv - Mathematics - Complex Variables

Abstract

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.