On the Fixed Point Method and Bloch’s Theorem

Abstract

In this paper, via the contraction mapping principle, we give a proof of a Bloch-type theorem for normalized harmonic Bochner–Takahashi K-mappings and for solutions to equations of the form $\mathit{P}\mathit{u}=0$, where P is a homogeneous differential operator with an analytic fundamental solution, that is, homogeneous elliptic operators with constant coefficients.