# CONTINUITY OF ONE-SIDED BEST SIMULTANEOUS APPROXIMATIONS

• Lee, Mun-Bae (DEPARTMENT OF MATHEMATICS, SOGANG UNIVERSITY) ;
• Park, Sung-Ho (DEPARTMENT OF MATHEMATICS, SOGANG UNIVERSITY) ;
• Rhee, Hyang-Joo (DEPARTMENT OF GENERAL STUDIES, DUKSUNG WOMEN’S UNIVERSITY)
• Published : 2000.11.01

#### Abstract

In the space $C_1(X)$ of real-valued continuous functions with $L_1-norm$, every bounded set has a relative Chebyshev center in a finite-dimensional subspace S. Moreover, the set function $F\rightarrowZ_S(F)$ corresponding to F the set of its relative Chebyshev centers, in continuous on the space B[$C_1(X)$(X)] of nonempty bounded subsets of $C_1(X)$ (X) with the Hausdorff metric. In particular, every bounded set has a relative Chebyshev center in the closed convex set S(F) of S and the set function $F\rightarrowZ_S(F)$(F) is continuous on B[$C_1(X)$ (X)] with a condition that the sets S(.) are equal.

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