Characterization of best uniform approximation with restricted ranges of derivatives
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This paper gives a general characterization theorem of a best uniform approximation of generalized polynomial having multiple restricted ranges of its derivatives. This theorem is widely applicable. The results on characterization in many standard approximations, such as approximation with Hermite-Birkhoff interpolatory side conditions, multiple comonotone approximation, and approximation by algebraic polynomials having bounded coefficients, etc., are special cases of our results.
KeywordsUniform Approximation Restrict Range Normed Linear Space Side Condition Algebraic Polynomial
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- Sippel, W., Approximation by Functions with Restricted Ranges, In: Lorentz, G.G. (ed.): Approximation Theory, New York: Academic Press, Inc. (1973), 481–484.Google Scholar