Abstract
n this paper, the relative widths of some sets in are studied. Relative widths is the further development of Kolmogorov widths and it is a new problem in approximation theory which aroused some mathematics workers great interest recently. We present some basic propositions of relative widths and investigate relative widths of some sets (ball or ellipsoid) of
Highlights
We present some basic propositions of relative widths and investigate relative widths of some sets (ball or ellipsoid) of l
The proof of Theorem 2 is complete
Summary
N. Konovalov in [1] first proposed the definition of relative widths which is in the sense of Kolmogorov. Let W and V be centrally symmetric sets in a Banach space X . The Kolmogorov n -dimensional widths of W relative to V in X (shortly, relative widths) is Where the infimum is taken over all n -dimensional subspaces Ln of X , n N .
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