Hyers and Ulam proved a stability result for convex functions, defined in a subset of W . Here we give an example showing that their result cannot be extended to those functions defined in infinite-dimensional normed spaces. Also, we give a positive result for a particular class of approximately convex functions, defined in a Banach space, whose norm satisfies the so-called convex approximation property.
A counterexample to the infinity version of the Hyers and Ulam stability theorem.
CASINI, EMANUELE GIUSEPPE;
1993-01-01
Abstract
Hyers and Ulam proved a stability result for convex functions, defined in a subset of W . Here we give an example showing that their result cannot be extended to those functions defined in infinite-dimensional normed spaces. Also, we give a positive result for a particular class of approximately convex functions, defined in a Banach space, whose norm satisfies the so-called convex approximation property.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
A counterexample to the infinity version of the Hyers and Ulam stability theorem..pdf
non disponibili
Tipologia:
Documento in Post-print
Licenza:
DRM non definito
Dimensione
508.05 kB
Formato
Adobe PDF
|
508.05 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
