A maximality theorem concerning extreme points

Concerning weak ∗ - extreme points

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak-extreme points of the unit ball is discrete.

A Theorem concerning Six Points

1. Introduction and statement of results. "Let three points be specified on a line. Then one of the points is in the interior of the line segment joining the other two, and one of the points is exterior to the line segment joining the other two." This elementary statement concerning the ordering of three points on a line is capable of various extensions. Thus, e.g., it is easy to prove the foll...

The starlikeness, convexity, covering theorem and extreme points of p-harmonic mappings

The main aim of this paper is to introduce three classes $H^0_{p,q}$, $H^1_{p,q}$ and $TH^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. First, we discuss the starlikeness and convexity of mappings in $H^0_{p,q}$ and $H^1_{p,q}$. Then establish the covering theorem for mappings in $H^1_{p,q}$. Finally, we determine the extreme points of the class $TH^*_{p}$.

the starlikeness, convexity, covering theorem and extreme points of p-harmonic mappings

the main aim of this paper is to introduce three classes $h^0_{p,q}$, $h^1_{p,q}$ and $th^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. first, we discuss the starlikeness and convexity of mappings in $h^0_{p,q}$ and $h^1_{p,q}$. then establish the covering theorem for mappings in $h^1_{p,q}$. finally, we determine the extreme points of the class $th^*_{p}$.

A Guide to the Ergodic Decomposition Theorem: Ergodic Measures as Extreme Points