Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces
We study the influence of computational errors on the convergence to compact sets of orbits of nonexpansive mappings in Banach and metric spaces. We first establish a convergence theorem assuming that the computational errors are summable and then provide examples which show that the summability of errors is necessary for convergence.
INEXACT ORBITS OF NONEXPANSIVE MAPPINGS
We study the influence of errors on the convergence of orbits of nonexpansive mappings in Banach and metric spaces.
A probabilistic proof of non-explosion of a non-linear PDE system
Using a representation in terms of a two-type branching particle system, we prove that positive solutions of the system remain bounded for suitable bounded initial conditions, provided A and B generate processes with independent increments and one of the processes is transient with a uniform power decay of its semigroup. For the case of symmetric stable processes on R 1,this answers a question raised in [4].