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Generalized deviations and best approximation theory. (English) Zbl 1072.41015
The author introduces a generalization of the concept of deviation. The existence of a deviation is established for a given generalized mean. Furthermore, the necessary and sufficient conditions on the existence of a generalized mean for a given deviation is established.

MSC:
41A50 Best approximation, Chebyshev systems
41A52 Uniqueness of best approximation
41A28 Simultaneous approximation
60F10 Large deviations
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References:
[1] Light W., Lecture Notes in Math. 1169, in: Approximation Theory in Tensor Product Spaces (1985)
[2] Singer I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces (1970) · Zbl 0197.38601
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