A C1 function which is nowhere strongly paraconvex and nowhere semiconcave

• Autorzy: Zajicek L.
• Języki publikacji: EN

Abstrakty

EN

X be an infinite-dimensional Banach space which admits an equivalent Fréchet smooth norm (or, more generally, a C1 Lipschitz bump function). Then there exists a C1 Lipschitz function ƒ on X such that, on any open ball, ƒ is neither strongly paraconvex nor semiconcave. In particular, ƒ is approximately convex in the sense of Ngai, Luc and Thera, but it is not strongly paraconvex on any ball.

Słowa kluczowe

EN

approximately convex function; strongly α(·)-paraconvex function; semiconcave function; C1 function

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2007
• Tom: Vol. 36, no 3
• Strony: 803--810
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Zajicek L.

• Charles University, Faculty of Mathematics and Physics, Sokolovska 83, 186 75 Praha 8, Czech Republic,

Bibliografia

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