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Strong unicity versus modulus of convexity
Published online by Cambridge University Press: 17 April 2009
Extract
We show that a Banach space has modulus of convexity of power type p if and only if best approximants to points from straight lines are uniformly strongly unique of order p. Assuming that the space is smooth, we derive a characterisation of the best simultaneous approximant to two elements, and use the characterisation to prove that p–type modulus of convexity implies order p strong unicity of the simultaneous approximant.
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- Research Article
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- Copyright © Australian Mathematical Society 1994
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