# An implicit function theorem

@article{Jittorntrum1978AnIF, title={An implicit function theorem}, author={Krisorn Jittorntrum}, journal={Journal of Optimization Theory and Applications}, year={1978}, volume={25}, pages={575-577} }

Suppose thatF:D⊂Rn×Rm→Rn, withF(x0,y0)=0. The classical implicit function theorem requires thatF is differentiable with respect tox and moreover that ∂1F(x0,y0) is nonsingular. We strengthen this theorem by removing the nonsingularity and differentiability requirements and by replacing them with a one-to-one condition onF as a function ofx.

#### 57 Citations

An implicit function theorem: Comment

- Mathematics
- 1980

In Ref. 1, Jittorntrum proposed an implicit function theorem for a continuous mappingF:Rn ×Rm →Rn, withF(x0,y0)=0, that requires neither differentiability ofF nor nonsingularity of ∂xF(x0,y0). In the… Expand

An Implicit-Function Theorem for a Class of Nonsmooth Functions

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This paper introduces the concept of strong approximation of functions, and a related concept ofstrong Bouligand (B-) derivative, and employs these ideas to prove an implicit-function theorem for nonsmooth functions, applicable to a considerably wider class of functions than is the classical theorem. Expand

THE IMPLICIT FUNCTION THEOREM AND IMPLICIT PARAMETRIZATIONS

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We discuss a dierential equations treatment of the implicit functions problem. Our approach allows a precise and complete description of the solution, of continuity and dierentiability properties.… Expand

A Homological Version of the Implicit Function Theorem

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Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a… Expand

A Note on Implicit Functions in Locally Convex Spaces

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An implicit function theorem in locally convex spaces is proved. As an application we study the stability, with respect to a parameter , of the solutions of the Hammerstein equation in a locally… Expand

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A probabilistic proof of the local Lipschitz continuity for the optimal stopping boundary of a class of problems with state space, which is the only existing proof that relies exclusively upon stochastic calculus. Expand

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The implicit function theorem is a statement of the existence, continuity, and difierentiability of a function or set of functions. The theorem is closely related to the convergence of Newton’s… Expand

On global implicit function theorem

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Abstract We study some certain maximal implicit functions and we apply our results to prove the local and global existence and local unicity of the solutions of the corresponding differential… Expand

On the Cauchy problem for planar autonomous Hamiltonian Systems with a discontinuous right-hand side

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Using the implicit function theorem for non-differentiable functions and structural properties of the dynamical system, we prove a local existence and uniqueness result for a class of planar… Expand

Brockett ’ s Theorem and Coron ’ s Condition

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ABSTRACT. Feedback asymptotic stabilization of nonlinear control systems is an important topic of control theory and applications. Broadly speaking, if the system • x = f(x, u) is locally… Expand

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