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Regularity theorems for harmonic functions

Ganenkova E. G., Starkov V. V.

Journal of Applied Analysis

2015

Vol. 21, nr 1

25--36

The regularity theorem is a result stating that functions which have extremal growth or decrease in the given class display a regular behaviour. Such theorems for linearly invariant families of analytic functions are well known. We prove regularity theorems for some classes of harmonic functions. Many presented statements are new even in the analytic case.

K-subquadratic set-valued functions

Troczka-Pawelec K.

Commentationes Mathematicae

2014

Vol 54, No. 2

147--157

Let X=(X,+) be an arbitrary topological group. The aim of the paper is to prove a regularity theorem for K-subquadratic set-valued functions, that is, solutions of the inclusion 2F(s)+2F(t)⊂F(s+t)+F(s−t)+K,s,t∈X, with values in a topological vector space and where K is a cone in this space.

Continuity of subquadratic set-valued functions

Troczka-Pawelec K.

Demonstratio Mathematica

2012

Vol. 45, nr 4

939-946

Let X = (X, +) be an arbitrary topological group. The aim of the paper is to prove a regularity theorem for set valued subquadratic functions, that is solutions of the inclusion (…), with values in a topological vector space.