Triangular mean-value functional equation

Abstract

The main objective of this thesis is to determine the general solution of the triangular mean-value functional equation with the constrain that for each triangle obtained by translations and dilations of an arbitrary fixed triangle, the value of the function at its centroid is the arithmetic mean of its values at the vertices. In particular, we obtain a general solution to the equation [Equation] for all z∈R² and t >0 where z₁,z₂,z₃ are fixed points in R².