Quantitative Estimates for $L^p$-Approximation by Bernstein-Kantorovich-Choquet Polynomials with Respect to Distorted Lebesgue Measures

Abstract

For the univariate Bernstein-Kantorovich-Choquet polynomials written in terms of the Choquet integral with respect to a distorted probability Lebesgue measure, we obtain quantitative approximation estimates for the $L^{p}$-norm, $1\le p<+\infty$, in terms of a $K$-functional.

Keywords

• {Monotone and submodular set function,Choquet integral,Bernstein-Kantorovich-Choquet polynomial,$L^{p}$ quantitative estimates,$K$-functional,Distorted Lebesgue measure

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