On local convexity of nonlinear mappings between Banach spaces

• Autorzy: Iryna Banakh , Taras Banakh , Anatolij Plichko , Anatoliy Prykarpatsky
• Języki publikacji: EN

Abstrakty

EN

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 ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.

Słowa kluczowe

EN

Locally convex mapping; Hilbert and Banach spaces; Modulus of convexity; Modulus of smoothness; Lipschitzopen maps

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 58C20: Differentiation theory (Gateaux, Fr\'echet, etc.)
• 52A41: Convex functions and convex programs
• 49J50: Fr\'echet and Gateaux differentiability

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 2264-2271

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Iryna Banakh

• Ya. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of National Academy of Sciences, 3b Naukova Str., 79060, Lviv, Ukraine

autor

Taras Banakh

autor

Anatolij Plichko

• Cracow University of Technology, Warszawska 24, 31-155, Kraków, Poland

autor

Anatoliy Prykarpatsky

• AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0101-z