An infinitesimal proof of the implicit function theorem
نویسندگان
چکیده
منابع مشابه
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There is the work by Bridges et al (1999) on the key features of a constructive proof of the implicit function theorem, including some applications to physics and mechanics. For mixtures of logistic distributions such information is lacking, although a special instance of the implicit function theorem prevails therein. The theorem is needed to see that the ridgeline function, which carries info...
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denote the open ball of radius a centred on the origin in IR. If the function ~g : Ba → IR d obeys there is a constant G < 1 such that ‖~g(~x)− ~g(~y)‖ ≤ G ‖~x− ~y‖ for all ~x, ~y ∈ Ba (H1) ‖~g(~0)‖ < (1−G)a (H2) then the equation ~x = ~g(~x) has exactly one solution. Discussion of hypothesis (H1): Hypothesis (H1) is responsible for the word “Contraction” in the name of the theorem. Because G <...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1993
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s001708950000971x