• The Mathematical Education
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• v.22 no.3
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• pp.57-58
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• 1984

• The Pure and Applied Mathematics
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• v.10 no.1
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• pp.49-56
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• 2003

For (equation omitted) be an ordered $\ell$(t)-tuple of numbers in｛1,2, …,$\ell$｝and let Tt be chosen from a finite composition of orthogonal projections (equation omitted) acting on the normed linear space $C_1$(X) to closed convex subset $S(fi_{j}\;^{t})$ respectively. In this paper, we study the convergence of the sequence (equation omitted) where (equation omitted).

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.743-753
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• 2000

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.