Abstract
Vector approximation problems are abstract approximation problems where a vectorial norm is used instead of a usual (real-valued) norm. Many important results known from approximation theory can be extended to this vector-valued case. After a short introduction we examine the relationship between vector approximation and simultaneous approximation, and we present the so-called generalized Kolmogorov condition. Moreover, we consider nonlinear and linear Chebyshev vector approximation problems and we formulate a generalized alternation theorem for these problems.
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© 2011 Springer-Verlag Berlin Heidelberg
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Jahn, J. (2011). Vector Approximation. In: Vector Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17005-8_9
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DOI: https://doi.org/10.1007/978-3-642-17005-8_9
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17004-1
Online ISBN: 978-3-642-17005-8
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