Extreme points in spaces of polynomials

Extreme and Exposed Points of Spaces of Integral Polynomials

We show that if E is a real Banach space such that E′ has the approximation property and such that `1 6↪→ ⊗̂ n,s, E then the set of extreme points of the unit ball of PI(E) is equal to {±φn : φ ∈ E′, ‖φ‖ = 1}. Under the additional assumption that E′ has a countable norming set we see that the set of exposed points of the unit ball of PI(E) is also equal to {±φn : φ ∈ E′, ‖φ‖ = 1}.

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 and Rotundity of Orlicz-sobolev Spaces

Extreme points of the unit cell Lebesgue-Bochner function spaces

On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...