Pointwise Approximation Theorems for Combinations of Bernstein Polynomials with Inner Singularities

Wenming Lu, Lin Zhang

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DOI: 10.4236/am.2011.24047                

Abstract

It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we give the Bernstein-Markov inequalities with step-weight functions for combinations of Bernstein polynomials with inner singularities as well as direct and inverse theorems.

Keywords

Bernstein Polynomials, Inner Singularities, Pointwise Approximation, Bernstein-Markov Inequalities, Direct and Inverse Theorems

Conflicts of Interest

The authors declare no conflicts of interest.

References

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