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A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation $$\dfrac{\overline{f_{ \overline{z}}}}{\overline{f}}=a\dfrac{f_{z}}{f}$$ f z ¯ ¯ f ¯ = a f z f . In this paper we investigate the univalence of logharmonic mappings of the form $$ f=zH\overline{G},$$ f = z H G ¯ , where H and G are analytic on a linearly connected domain. We discuss the relation with the univalence of its analytic counterparts. Stable Univalence and its consequences are also considered.
Analysis and Mathematical Physics – Springer Journals
Published: May 22, 2019
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