Comparison theorems using general cones for norms of iteration matrices (Q1772728)

Description of the paper: Among other preliminaries, in Section 2 the authors introduce the classes of cone absolute norms, cone linear absolute norms and cone max norms in order to put their results in a setting of a proper, but otherwise general, cone in finite dimensional real space. The authors principal results are contained in Section 3. In Section 4 they obtain some analogous results for right weak regular splittings which are the duals of the theorems in Section 3. In Section 5 they derive a comparison theorem for spectral radii, and, turning to a different approach, they give a proof of the well-known theorem in a cone setting which relies on order and convergence properties of operators without any appeal to Perron-Frobenius theory.