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<p>We present a generalization of the inverse mapping theorem, where variations of a weaker non-expansiveness property (referred to as property <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\textsf {A}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">A</mi> </math></EquationSource> </InlineEquation>) replace the key <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textsf {C}^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="sans-serif">C</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> condition. We also obtain inverse mapping theorems that can be applied to non-smooth maps. Also as a by-product of the generalized inverse mapping theorem, we prove generalizations of the implicit function theorem and existence and uniqueness theorem of abstract PDE systems as well.</p>

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A Generalization of the Inverse Mapping Theorem in Infinite Dimensions

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Sajjad Lakzian

摘要

We present a generalization of the inverse mapping theorem, where variations of a weaker non-expansiveness property (referred to as property \({\textsf {A}}\) A ) replace the key \(\textsf {C}^1\) C 1 condition. We also obtain inverse mapping theorems that can be applied to non-smooth maps. Also as a by-product of the generalized inverse mapping theorem, we prove generalizations of the implicit function theorem and existence and uniqueness theorem of abstract PDE systems as well.