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Local Topological Properties of Differentiable Mappings (Singularities of Differentiable Mappings)

Local Topological Properties of Differentiable Mappings (Singularities of Differentiable Mappings)
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Mapping Differentiated Integration

2020
This chapter maps the development of differentiated integration over the entire history of the EU and across all member states and policies. It shows that differentiation has been on the rise in treaty law and legislation. Yet, relative to the dramatic growth in EU authority and member states over time, there is no evidence for a trend towards ‘ever ...
Frank Schimmelfennig, Thomas Winzen
exaly   +2 more sources

The Image of a Weakly Differentiable Mapping

SIAM Journal on Mathematical Analysis, 2004
Summary: Let \(\Omega \subset\mathbb{R}^n\) be an open ball, \(n \geq 2\). Suppose that \(f,g : \Omega \to\mathbb{R}^n\), \(f = g\) on \(\partial\Omega\), and that \(f\) is injective. In the case that \(f\) and \(g\) are continuous, then \(f(\overline{\Omega}) \subset g(\overline{\Omega})\).
David Swanson, William P. Ziemer
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Differential Inclusions for fuzzy maps

Fuzzy Sets and Systems, 2000
From the authors abstract: The authors introduce the problems of differential inclusions for fuzzy maps, and prove the existence of solutions to these problems by the continuous selection theorem and fixed point theorems, respectively.
Yuanguo Zhu, Ling Rao
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The s-differentiability of a fuzzy-valued mapping

Information Sciences, 2003
A new concept of the differentiability of fuzzy-valued mappings is presented (\(s\)-differentiability), which utilizes the differential for a Banach space-valued mapping. Connections between the De Blasi differentiability and \(s\)-differentiability, and between the \(\pi\)-differentiability and \(s\)-differentiability are studied. It is shown that the
Luis J. Rodríguez-Muñiz, Miguel López-Díaz, María Angeles Gil, Dan A. Ralescu   +3 more
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On differentiability and surjectivity of α-lipschitz mappings

Annali di Matematica Pura ed Applicata, 1974
In the first part of this paper the well known result that the Frechet differential and the asymptotic derivative of a compact mapping is compact, is extended to α-Lipschitz mappings (see Theorem1.1, 1.2 and Corollaries).
PEJSACHOWICZ, JACOBO, Vignoli A.
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Differential subordination and conformal mappings

Complex Variables, Theory and Application: An International Journal, 1989
Suppose that N(z), D(z) are functions analytic in the unit disc \(\Delta\), \(N(0)=D(0)=0\) and that D(z) maps \(\Delta\) onto a domain starlike w.r.t. the origin. The subject of this paper is to impose a sufficient condition on D(z) which guarantee that the implication \[ Re\{N'(z)/D'(z)\}>0\quad \Rightarrow \quad Re\{N(z)/D(z)\}>\alpha >0 \] holds in
Karunakaran, V., Ponnusamy, S.
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The Mapping of Differentiation

1974
Using Theorem 8.1, we shall derive, in this Chapter, Theorem 9.1, which provides the image of differentiation. The latter will prove extremely useful in practical applications of the L-transformation. A few introductory remarks will aid the subsequent development.
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On a Domain of Invertibility of a Differentiable Mapping

Quaestiones Mathematicae, 2003
This paper deals with a domain and its range of invertibility of a differentiable mapping at a point with an invertible derivative. Assuming the C2-class of a mapping T defined in a neighbourhood of a point x0 in Banach space with an invertible derivative, we look for estimations of radii of balls with centers in x0 and T (x0) which are contained in a ...
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