Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A quantitative version of the converse Taylor theorem: $C^{k,ω}$-smoothness

100%

Johanis M.

Colloquium Mathematicum

2014

tom 136

nr 1

57-64

We prove a uniform version of the converse Taylor theorem in infinite-dimensional spaces with an explicit relation between the moduli of continuity for mappings on a general open domain. We show that if the domain is convex and bounded, then we can extend the estimate up to the boundary.

Smooth approximations without critical points

63%

Hájek P., Johanis M.

Open Mathematics

2003

tom 1

nr 3

284-291

In any separable Banach space containing c 0 which admits a C k-smooth bump, every continuous function can be approximated by a C k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains a set residual in some neighbourhood of zero.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

2 Johanis M.

1 Hájek P.

1 2014

1 2003

Wyniki wyszukiwania

A quantitative version of the converse Taylor theorem: $C^{k,ω}$-smoothness

Smooth approximations without critical points