Abstract
We characterize best simultaneous approximation from convex sets, in terms of onesided Gateaux derivatives, using the ℓ 1 and ℓ ∞ vectorial norms, in a general setting and in L 1 . In L 1 , we give necessary and sufficient conditions for uniqueness. We show that p -type modulus of convexity implies order p -strong unicity of the best ℓ ∞ simultaneous approximation.
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