Yayınlanmış 1 Ocak 2012
| Sürüm v1
Dergi makalesi
Açık
On local convexity of nonlinear mappings between Banach spaces
- 1. Natl Acad Sci, Ya Pidstryhach Inst Appl Problems Mech & Math, UA-79060 Lvov, Ukraine
- 2. Cracow Univ Technol, PL-31155 Krakow, Poland
- 3. AGH Univ Sci & Technol, PL-30059 Krakow, Poland
Açıklama
We find conditions for a smooth nonlinear map f: U -> V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive E > < c the image f(B (E >)(x)) of each E >-ball B (E >)(x) aS, U is convex. We give a lower bound on c via the second order Lipschitz constant Lip(2)(f), the Lipschitz-open constant Lip(o)(f) of f, and the 2-convexity number conv(2)(X) of the Banach space X.
Dosyalar
bib-af0e81ab-ec29-4f05-b431-81042541bd63.txt
Dosyalar
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