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arXiv · 2308.08081

Prawitz's area theorem and the mixed Aharonov sequence

Jianjun Jin
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Abstract

In this paper, motivated by the Prawitz area theorem and the work of Aharonov, we introduce the mixed Aharonov sequence associated with a locally univalent analytic function. By using the mixed Aharonov sequence, we establish a new univalence criterion for the locally univalent analytic functions in the unit disk, which generalizes some related results of Aharonov in \cite{Ah}. We also prove some new properties about the (mixed) Aharonov sequence, in particular, a new inequality for the Aharonov sequence is established for the univalent functions with a quasiconformal extension.

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Jianjun Jin. 2023-08-16. Prawitz's area theorem and the mixed Aharonov sequence. https://arxiv.org/abs/2308.08081

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