A weak ergodic theorem for infinite products of Lipschitzianmappings

[摘要] LetKbe a bounded, closed, and convex subset of a Banachspace. For a Lipschitzian self-mappingAofK, we denote byLip(A)its Lipschitz constant. In this paper, we establish aconvergence property of infinite products of Lipschitzianself-mappings ofK. We consider the set of all sequences{At }t=1∞of such self-mappings with the propertylimsupt→∞Lip(At )≤1. Endowing it with an appropriate topology, we establish a weak ergodictheorem for the infinite products corresponding to generic sequences in this space.

[学科分类] 数学（综合）