On strong unicity of -approximation

Author:
András Kroó

Journal:
Proc. Amer. Math. Soc. **83** (1981), 725-729

MSC:
Primary 41A52

DOI:
https://doi.org/10.1090/S0002-9939-1981-0630044-4

MathSciNet review:
630044

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Abstract: Let be the space of continuous functions on with norm , and let be a finite dimensional unicity subspace, i.e. any possesses a unique best approximation out of . Consider an arbitrary such that 0 is its best approximation. Then for any and with it follows that , where and denotes the modulus of continuity of . ( is used to denote the inverse function.)

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0630044-4

Article copyright:
© Copyright 1981
American Mathematical Society