Note on the best approximation in $L^1$ metric
arXiv:1607.05246h-index: 2
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Provides a theoretical result for approximation theory, but is incremental as it extends known methods to a specific inequality.
The paper presents an approach for best approximation by trigonometric polynomials in L1 metric and applies it to find optimal constants in Nikolsky-type inequalities for Lipschitz functions approximated by algebraic polynomials.
We present one of the approaches to find the best approximation of the given function by trigonometric polynomials in $L^1$ metric and applied it to find the optimal constants in the Nikolsky's type inequality, concerning approximation of Lipschitz functions by algebraic polynomials.