Abstract
In this chapter we investigate certain vector approximation problems, which are approximation problems where a vectorial norm is used instead of a usual (real-valued) norm. About 50 years ago vectorial norms were first introduced by Kantorovitch (Ref. 1), who developed a mathematical theory of linear spaces equipped with a vectorial norm. Many important results known from approximation theory (e.g., see Refs. 2, 3) can be extended to this vector-valued case (compare Ref. 4). In this chapter we present an application-oriented approach to vector approximation and we do not intend to formulate the results in the most general way. Therefore, we develop the proofs also in this special setting, although several results could be deduced from a general theory of vector approximation.
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References
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© 1988 Springer Science+Business Media New York
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Jahn, J., Krabs, W. (1988). Applications of Multicriteria Optimization in Approximation Theory. In: Stadler, W. (eds) Multicriteria Optimization in Engineering and in the Sciences. Mathematical Concepts and Methods in Science and Engineering, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3734-6_3
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DOI: https://doi.org/10.1007/978-1-4899-3734-6_3
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