Remarks on the Belitskii–Lyubich and discrete Markus–Yamabe conjectures

Abstract

Abstract In this paper we prove the Belitskii–Lyubich conjecture for triangular and gradient mappings. These results resemble those obtained for the discrete Markus–Yamabe conjecture. However, the proofs are quite different, which sheds new light on the subject. We complete the picture by showing that the general versions of the two conjectures can be turned into theorems at little cost, simply by relaxing their spectral condition.