Best simultaneous approximation to totally bounded sequences in Banach spaces

This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.National Natural Science Foundation of ChinaProgram for New Century Excellent Talent in UniversityDirección General de Investigación Científica y TécnicaJunta de Andalucí