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The notion of a firmly nonexpansive mapping is central in fixed point theorybecause of attractive convergence properties for iterates and thecorrespondence with maximal monotone operators due to Minty. In this paper, wesystematically analyze the relationship between properties of firmlynonexpansive mappings and associated maximal monotone operators. Dual andself-dual properties are also identified. The results are illustrated throughseveral examples.

Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality