Otevřenost a diferencovatelnost zobrazení

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F08%3A00501247" target="_blank" >RIV/49777513:23520/08:00501247 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Openness and differentiability of mappings

Popis výsledku v původním jazyce

We prove a generalization of the well-known Robinson-Ursescu Theorem and of Graves' Theorem in case that the set of admissible solutions is not the whole space but the closed convex set only. We explore the relationship between the openness of a nonlinear mapping and the openness of its suitable linear approximation We illustrate several application: the optimization theory, the constrained local controllability of nonlinear dynamical systems, and finding a differentiable selection of the inverse mapping; in the fifth chapter. We prove that if the norm on a Banach space in question is both differentiable and locally uniformly rotund, then the infimal convolution is differentiable on a residual set, provided that it is attained at densely many points.

Název v anglickém jazyce

Openness and differentiability of mappings

Popis výsledku anglicky

We prove a generalization of the well-known Robinson-Ursescu Theorem and of Graves' Theorem in case that the set of admissible solutions is not the whole space but the closed convex set only. We explore the relationship between the openness of a nonlinear mapping and the openness of its suitable linear approximation We illustrate several application: the optimization theory, the constrained local controllability of nonlinear dynamical systems, and finding a differentiable selection of the inverse mapping; in the fifth chapter. We prove that if the norm on a Banach space in question is both differentiable and locally uniformly rotund, then the infimal convolution is differentiable on a residual set, provided that it is attained at densely many points.

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2008

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů