Pseudo-contractions, rigidity, fixed points and related questions

Daniel Alpay; Vladimir Bolotnikov; David Shoikhet

doi:10.1007/s13324-019-00346-2

Pseudo-contractions, rigidity, fixed points and related questions

Daniel Alpay
, Vladimir Bolotnikov
, David Shoikhet

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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).

Original language	English
Article number	7
Journal	Analysis and Mathematical Physics
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/s13324-019-00346-2
State	Published - 1 Mar 2020
Externally published	Yes

Keywords

Angular derivative
Denjoy–Wolff point
Pseudo-contraction

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

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10.1007/s13324-019-00346-2

Cite this

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title = "Pseudo-contractions, rigidity, fixed points and related questions",

abstract = "The class of holomorphic self-mappings of the open unit disk (which are contractions with respect to the Poincar{\'e} 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).",

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AU - Bolotnikov, Vladimir

AU - Shoikhet, David

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N2 - 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).

AB - 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).

KW - Angular derivative

KW - Denjoy–Wolff point

KW - Pseudo-contraction

UR - https://www.scopus.com/pages/publications/85077206898

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DO - 10.1007/s13324-019-00346-2

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IS - 1

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ER -

Pseudo-contractions, rigidity, fixed points and related questions

Abstract

Keywords

ASJC Scopus subject areas

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