Note on the convolution of harmonic mappings

Abstract

Dorff et al. \cite{DN} formulated a question concerning the convolution of two right half-plane mappings, where the normalization of the functions was considered incorrectly. In this paper, we have reformulated the open problem in correct form and provided a solution to it in a more general form. In addition, we also obtain two new theorems which correct and improve some other results.

11 pages; An extended version of this article was in a couple of conferences, and also in later workshops in Chennai during 2017 in India. This version will appear in Bulletin of the Australian Mathematical Society