 Firmly nonexpansive mapping

ID: firmly-nonexpansive-mapping

A mapping

T

on an inner-product space is firmly nonexpansive when

∥ T (v) - T (w) ∥^{2} \leq ⟨ T (v) - T (w), v - w ⟩ .

Every firmly nonexpansive mapping is nonexpansive, and the resolvent of a maximal monotone operator is firmly nonexpansive.

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