Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality

Details Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality

2011-01-24

arxiv.org/abs/1101.4688v1

Mathematics

Functional Analysis

Scientific paper

The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically analyze the relationship between properties of firmly nonexpansive mappings and associated maximal monotone operators. Dual and self-dual properties are also identified. The results are illustrated through several examples.

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