Bolzano's theorems for holomorphic mappings

DOI10.1007/S11401-017-1083-8zbMath1366.30005OpenAlexW2593077007MaRDI QIDQ2358537

Jean Mawhin

Publication date: 15 June 2017

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-017-1083-8

zbMATH Keywords

Brouwer degreeBrouwer fixed point theoremCauchy's theoremBolzano's theoremHadamard-Shih's conditionsPoincaré-Miranda conditions

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Fixed points and coincidences in algebraic topology (55M20)

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Cites Work

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• A note on topological degree theory for holomorphic maps
• Bolzano's Theorem in Several Complex Variables
• An Analog of Bolzano's Theorem for Functions of a Complex Variable
• The Poincare-Miranda Theorem
• A Simple Approach to Brouwer Degree Based on Differential Forms
• Variations on Poincaré-Miranda’s Theorem

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