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Abstract
The main object of this paper is to investigate the univalence of certain polyharmonic mappings under differential operator. We first establish two versions of integral inequality for harmonic mappings. Then, using these results, we obtain six versions of Bloch–Landau type theorems for certain polyharmonic mappings of the form L ( F ) = z F z − z ¯ F z ¯ , where F are normalized polyharmonic mappings in the unit disk, which improve the related results of earlier authors.
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