Two-point distortion theorems for harmonic mappings

preprint2022arXivOpen access

Abstract

We establish two-point distortion theorems for sense-preserving planar harmonic mappings f=h+g‾f=h+\overline{g} which satisfies the univalence criteria in the unit disc such that, Becker's and Nehari`s harmonic version. In addition, we find the sharp two-point distortion theorem when hh is a convex function, and normalized mappings such that $h(\D)$ is a cc-linearly connected domain. To do this, we use the order of this family.

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