Author(s)

Wenming Lu, Lin Zhang

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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.

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

W. Lu and L. Zhang, "Pointwise Approximation Theorems for Combinations of Bernstein Polynomials with Inner Singularities," Applied Mathematics, Vol. 2 No. 4, 2011, pp. 389-397. doi: 10.4236/am.2011.24047.