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The class of holomorphic self-mappings of the open unit disk (which are contractions with respect to the Poincaré metric) admits a natural extension to the class of holomorphic pseudo-contractions. In this paper, we study various inequalities involving the values of derivatives of holomorphic pseudo-contractions at fixed points (particularly, at the Denjoy–Wolff fixed point).


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Analysis and Mathematical Physics, volume 10, in 2020 following peer review. The final publication may differ and is available at Springer via

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