A right inverse function theorem without assuming differentiability (Q2714210)
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scientific article; zbMATH DE number 1604042
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A right inverse function theorem without assuming differentiability |
scientific article; zbMATH DE number 1604042 |
Statements
12 June 2001
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open mapping theorem
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modulus of continuity
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modulus of openness
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Brouwer's fixed-point theorem
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tangent function
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A right inverse function theorem without assuming differentiability (English)
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An inverse function theorem in Euclidean spaces is proved for functions which are at some point `near to a local homeomorphism'. No differentiability is required, but instead only estimates for the modulus of continuity resp. openness of the involved functions. For the corresponding open mapping theorem, and more general, the existence of a local right-inverse with reasonable additional properties, only a pointwise condition is required. This part is based on Brouwer's fixed-point theorem and generalizes theorems of \textit{T. Szilágyi} [Ann. Univ. Sci. Budapest. Rolando Eötvös, Sect. Math. 20, 107-110 (1977; Zbl 0374.26011)] and \textit{H. Halkin} [SIAM J. Control 12, 229-236 (1974; Zbl 0285.90070)]. There is some connection with a result of \textit{M. Radulescu and S. Radulescu} [J. Math. Anal. Appl. 138, 581-590 (1989; Zbl 0745.58008)].
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