On a result of Pazy concerning the asymptotic behaviour of nonexpansive mappings
Heinz H. Bauschke, Graeme R. Douglas, Walaa M. Moursi
TL;DR
This paper examines Pazy's 1971 trichotomy result on nonexpansive mappings, focusing on fixed-point free cases, and provides evidence supporting the conjecture that iterates always converge cosmically.
Contribution
It offers a detailed analysis of fixed-point free nonexpansive mappings and presents new results and examples that support the conjecture of cosmic convergence.
Findings
Supports the conjecture of cosmic convergence for nonexpansive mappings
Provides new examples illustrating asymptotic behaviors
Analyzes fixed-point free cases in detail
Abstract
In 1971, Pazy presented a beautiful trichotomy result concerning the asymptotic behaviour of the iterates of a nonexpansive mapping. In this note, we analyze the fixed-point free case in more detail. Our results and examples give credence to the conjecture that the iterates always converge cosmically.
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