In this paper, we consider linear combinations of harmonic K-quasiregular mappings fⱼ=hⱼ+ḡⱼ $(j=1, 2)$ of the class Har (k; φⱼ), where k∈ [0,1), \|ωfⱼ\|∞=\|g'ⱼ/h'ⱼ\|∞≤ k<1, $k=(1-K)/(1+K)$, and φⱼ=hⱼ+eiθgⱼ is a univalent analytic function. We provide sufficient conditions for the linear combinations of mappings in these classes to be univalent and for the image domains to be linearly connected. Furthermore, we consider under which conditions the linear combination f is bi-Lipschitz.
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Huang et al. (2024) studied this question.
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