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Best approximation by polynomials

Published online by Cambridge University Press:  17 April 2009

Sung Guen Kim
Sung Guen Kim
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu, Korea (702-701), e-mail: [email protected]
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Abstract

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In this paper we show that if E is a separable Banach space, F is a reflexive Banach space, and n, k ∈ ℕ, then every continuous polynomial of degree n from E into F has at least one element of best approximation in the Banach subspace of all continuous k–homogeneous polynomials from E into F.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 267 - 273
Copyright
Copyright © Australian Mathematical Society 2003

References

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