Nearly outer functions as extreme points in punctured Hardy spaces

Minimal Cut-Generating Functions are Nearly Extreme

We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory-Johnson setting, as well as a recent extension by Cornuéjols and Yıldız. We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal fu...

Extreme Points of Vector Functions

Several previous investigations have appeared in the literature which discuss the nature of the set T in »-dimensional space spanned by the vectors ifsdui, ■ ■ ■ , fsdp.n) where 5 ranges over all measurable sets. It was first shown by Liapounov that xi ui, • • ■ , un are atomless measures, then the set F is convex and closed. Extensions of this result were achieved by D. Blackwell [l] and Dvore...

Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces

We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study...

On the Extreme Points and Strongly Extreme Points in Köthe–bochner Spaces

We give the necessary conditions of extreme points and strongly extreme points in the unit ball of Köthe–Bochner spaces. The conditions have been shown to be sufficient earlier.

Extreme points of the unit cell in Lebesgue-Bochner functions spaces