Abstract
We continue studying the mappings that are close to the harmonic mappings (e-quasiharmonic mappings with e small). This study originates with the previous articles of the author. The results of the article include a theorem on connection between the notion of e-quasiharmonic mapping and the solutions to Beltrami systems, an analog to the arithmetic mean property of harmonic functions for e-quasiharmonic mappings, a theorem on stability in the Poisson formula for harmonic mappings in the ball, and a theorem on the local smoothing of e-quasiharmonic mappings with e small which preserves proximity to the harmonic mappings.
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