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A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation $$\dfrac{\overline{f_{ \overline{z}}}}{\overline{f}}=a\dfrac{f_{z}}{f}$$fz¯¯f¯=afzf. In this paper we investigate the univalence of logharmonic mappings… Click to show full abstract
A logharmonic mapping f is a mapping that is a solution of the nonlinear elliptic partial differential equation $$\dfrac{\overline{f_{ \overline{z}}}}{\overline{f}}=a\dfrac{f_{z}}{f}$$fz¯¯f¯=afzf. In this paper we investigate the univalence of logharmonic mappings of the form $$ f=zH\overline{G},$$f=zHG¯, 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.
Journal Title: Analysis and Mathematical Physics
Year Published: 2019
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