منابع مشابه
Implicit function theorem via the DSM
Sufficient conditions are given for an implicit function theorem to hold. The result is established by an application of the Dynamical Systems Method (DSM). It allows one to solve a class of nonlinear operator equations in the case when the Fréchet derivative of the nonlinear operator is a smoothing operator, so that its inverse is an unbounded operator. © 2009 Elsevier Ltd. All rights reserved.
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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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Robinson’s implicit function theorem has played a mayor role in the analysis of stability of optimization problems in the last two decades. In this paper we take a new look at this theorem, and with an updated terminology go back to the roots and present some extensions.
متن کاملThe Contraction Mapping Theorem and the Implicit Function Theorem
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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We prove computable versions of the Implicit Function Theorem in the single and multivariable cases. We use Type Two Effectivity as our foundation.
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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2010
ISSN: 0362-546X
DOI: 10.1016/j.na.2009.09.032