Generalized Bernstein-type approximation of continuous functions

TL;DR

This paper presents a precise, non-asymptotic error estimate for Bernstein-type approximations of continuous functions using modern probabilistic methods.

Contribution

It introduces a new sharp error bound for Bernstein approximations that is non-asymptotic and non-uniform, utilizing advanced probabilistic techniques.

Findings

Provides explicit error bounds for Bernstein approximation

Utilizes modern probabilistic tools for analysis

Enhances understanding of approximation accuracy

Abstract

We derive in this short article the non-asymptotical non-uniform sharp error estimation for the Bernstein's type approximation of continuous function based on the modern probabilistic apparatus.