The implicit function theorem in functional analysis
نویسندگان
چکیده
منابع مشابه
The Implicit Function Theorem and Implicit Parametrizations∗
We discuss a differential equations treatment of the implicit functions problem. Our approach allows a precise and complete description of the solution, of continuity and differentiability properties. The critical case is also considered. The investigation is devoted to dimension two and three, but extensions to higher dimension are possible. MSC: 26B10, 34A12, 53A05. keywords: implicit functio...
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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: Duke Mathematical Journal
سال: 1966
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-66-03347-3