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Strong unicity versus modulus of convexity

Published online by Cambridge University Press:  17 April 2009

Robert Huotari  and
Salem Sahab
Robert Huotari
Affiliation:
Department of Mathematics IdahoState UniversityPocatello ID 83209United States of America
Salem Sahab
Affiliation:
Mathematics Department PO Box 9028King Abdulaziz UniversityJeddah 21413Saudi Arabia
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 2 , April 1994 , pp. 305 - 310
Copyright
Copyright © Australian Mathematical Society 1994

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