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Full-Text Articles in Physical Sciences and Mathematics
A Duality Approach To Best Uniform Convex Approximation, S. E. Weinstein, Yuesheng Xu
A Duality Approach To Best Uniform Convex Approximation, S. E. Weinstein, Yuesheng Xu
Mathematics & Statistics Faculty Publications
Let C[a, b] be the space of continuous functions on [a, b] endowed with the uniform norm llƒll ∞ = sup{ Iƒ(x)1 :x∈ [a, b]}. Let K be the set of convex functions defined on [a, b]. A function g* ∈ K is said to be a best uniform convex approximation to ƒ ∈ C[a, b] if ∥ƒ - g*∥ ∞ = inf { ∥ƒ - g∥∞ : g ∈ K}.