Nonlinear weighted best simultaneous approximation in Banach spaces

The present paper is concerned with the problem of weighted best simultaneous approximations in Banach spaces. The weighted best simultaneous approximations to sequences from S- and BS-suns in the Banach space are characterized in view of the Kolmogorov conditions. Applications are provided for weig...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-01, Vol.337 (2), p.1100-1118
Main Authors: Luo, Xianfa, Li, Chong, Lopez, Genaro
Format: Article
Language:English
Subjects:
Characterization
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
RS-set
S-sun
Sciences and techniques of general use
Simultaneous approximation
Uniqueness
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Summary:The present paper is concerned with the problem of weighted best simultaneous approximations in Banach spaces. The weighted best simultaneous approximations to sequences from S- and BS-suns in the Banach space are characterized in view of the Kolmogorov conditions. Applications are provided for weighted best simultaneous approximations from RS-sets and strict RS-sets. Our results obtained in the present paper extend and improve all earlier known results in this direction.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.04.060