Regular points for $\alpha $-harmonic functions

Regular Points of Lipschttz Functions

Let/be a locally Lipschitz function on a Banach space X, and S a subset of X. We define regular (i.e. noncritical) points for / relative to S, and give a sufficient condition for a point z e S to be regular. This condition is then expressed in the particular case when/is C1, and is used to obtain a new proof of Hoffman's inequality in linear programming.

On the Critical Points of Harmonic Functions

Stability for certain subclasses of harmonic univalent functions

In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.

Polynomial Invariants and Harmonic Functions Related to Exceptional Regular Polytopes

regular polytopes, mean value property, finite reflection groups We compute certain polynomial invariants for the finite reflection groups of the types H3, H4 and F4. Using this result, we explicitly determine the solution space of functions satisfying a mean value property related to the exceptional regular polytopes, namely, the icosahedron and dodecahedron in three dimensions and the 24-cell...

A certain convolution approach for subclasses of univalent harmonic functions

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.