Note on the convolution of harmonic mappings

TL;DR

This paper corrects and generalizes previous work on the convolution of harmonic mappings, providing a proper formulation of an open problem and introducing new theorems that enhance existing results.

Contribution

It reformulates an open problem on harmonic mappings convolution correctly and offers a more general solution along with two new theorems that improve prior results.

Findings

Corrected the formulation of the convolution problem for harmonic mappings

Provided a more general solution to the open problem

Introduced two new theorems improving existing results

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.