Generalizations of harmonic functions in $${\mathbb R}^m$$

In recent works, arbitrary structural sets in the non-commutative Clifford analysis context have been used to introduce non-trivial generalizations of harmonic algebra valued functions $\mathbb{R}^m$. Being defined as solutions elliptic (generally non-strongly elliptic) partial differential equations, $(\varphi,\psi)$-inframonogenic and $(\varphi,\psi)$-harmonic do not share good structure properties ones. The aim this paper it show clarified relationship between these classes functions.