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Inverse Mapping Theorem on Coordinate Spaces
Author(s) -
Ma TsoyWo
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1017/s0024609301008050
Subject(s) - mathematics , bounded inverse theorem , inverse function theorem , fréchet space , open mapping theorem (functional analysis) , banach space , locally convex topological vector space , pure mathematics , inverse , danskin's theorem , mean value theorem (divided differences) , brouwer fixed point theorem , closed graph theorem , kelvin–stokes theorem , eberlein–šmulian theorem , mathematical analysis , interpolation space , fixed point theorem , lp space , picard–lindelöf theorem , topological space , functional analysis , finite rank operator , geometry , biochemistry , chemistry , gene
A mean‐value theorem, an inverse mapping theorem and an implicit mapping theorem are established here in a class of complex locally convex spaces, including the spaces of test functions in distribution theory. Our main tool is the integral formula and the invariance of the domain, derived from topological degrees, rather than from fixed points of contractions in Banach spaces.