Convolutions of Harmonic Half-Plane Mappings with Harmonic Vertical Strip Mappings

Zhihong Liu, Yueping Jiang, Yong Sun

In the present paper, we prove the convolutions of generalized harmonic right half-plane mappings with harmonic vertical strip mappings are univalent and convex in the horizontal direction. Moreover, some examples of harmonic univalent mappings convex in the horizontal direction are also constructed to illuminate the main results.