Finite Dimensional Chebyshev Subspaces of Banach Spaces

Finite Dimensional Chebyshev Subspaces of Banach Spaces

Extreme Points Metric Projection Chebyshev Subspaces (Uniquenes, Characterization & Existence)

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A Chebyshev set is a subset of a normed linear space that admits unique best approximations. In 1853, the Russian mathematician Chebyshev asked the question: "can we represent any continuous function defined on [a,b] by a polynomial, of degree at most n, in such a way that the maximum error at any point in [a,b] is controlled?" Since then, the mathematicians have searched : why such a polynomial should exist? If it does, can we hope to construct it? If it exists, is it also unique? What happens if we change the measure of error? The aim of this book is to study finite dimensional Chebyshev sub...