On Holomorphic Self-Maps of a Disk with Fixed Points

V. N. Dubinin

doi:10.1134/s1995080225614225

February 1, 2026Lobachevskii Journal of Mathematics

On Holomorphic Self-Maps of a Disk with Fixed Points

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Key Points

To derive Cowen and Pommerenke inequalities for holomorphic maps of a disk with fixed points using the Lindelof principle and capacity approach.
Application of the Lindelof principle
Utilization of the capacity approach
Derivation of inequalities for holomorphic maps
Demonstrated the Cowen and Pommerenke inequalities for holomorphic maps
Generalizations of these inequalities for maps with fixed points were established

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Implication

Application of Lindelof principle reveals inequalities in holomorphic maps of a disk with fixed points.

Abstract

We present an application of the Lindelof principle and the capacity approach to deriving the well-known Cowen and Pommerenke inequalities and their generalizations for holomorphic maps of a disk into itself with fixed points.

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V. N. Dubinin (2026) studied this question.

synapsesocial.com/papers/6a338e14630953a74978eda6 https://doi.org/10.1134/s1995080225614225

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On Holomorphic Self-Maps of a Disk with Fixed Points

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Implication

Abstract

Discussion

Cite This Study

On Holomorphic Self-Maps of a Disk with Fixed Points

Key Points

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Implication

Abstract

Discussion

Cite This Study

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