Monatshefte für Mathematik ( IF 0.933 ) Pub Date : 2020-06-29 , DOI: 10.1007/s00605-020-01442-3
Md Firoz Ali, Vasudevarao Allu, Nirupam Ghosh

We consider the convolution of right half-plane harmonic mappings in the unit disk $$\mathbb {D}:=\{z\in \mathbb {C}:\, |z|<1\}$$ with respective dilatations $$e^{i \alpha }(z + a)/(1 + a z)$$ and $$-z$$, where $$-1< a < 1$$ and $$\alpha \in \mathbb {R}$$. We prove that such convolutions are locally univalent and convex in the horizontal direction under certain condition.

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