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| Bolzano's Theorems for Holomorphic Mappings |
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Citation： |
Jean MAWHIN.Bolzano's Theorems for Holomorphic Mappings[J].Chinese Annals of Mathematics B,2017,38(2):563~578 |
| Page view： 612
Net amount： 540 |
Authors： |
Jean MAWHIN; |
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| Abstract： |
The existence of a zero for a holomorphic functions on a ball or on
a rectangle under some sign conditions on the boundary generalizing
Bolzano's ones for real functions on an interval is deduced in a
very simple way from Cauchy's theorem for holomorphic functions. A
more complicated proof, using Cauchy's argument principle, provides
uniqueness of the zero, when the sign conditions on the boundary are
strict. Applications are given to corresponding Brouwer fixed
point theorems for holomorphic functions. Extensions to holomorphic
mappings from $\Cn$ to $\Cn$ are obtained using Brouwer degree. |
Keywords： |
Holomorphic function, Hadamard-Shih's conditions,Poin-ca-r'e---Mi-ran-da's conditions, Bolzano's theorem,Cauchy's theorem, Brouwer fixed point theorem, Brouwer degree |
Classification： |
30C15, 30E20, 55M20 |
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