TITLE:
Pointwise Approximation Theorems for Combinations of Bernstein Polynomials with Inner Singularities
AUTHORS:
Wenming Lu, Lin Zhang
KEYWORDS:
Bernstein Polynomials, Inner Singularities, Pointwise Approximation, Bernstein-Markov Inequalities, Direct and Inverse Theorems
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.4,
March
31,
2011
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.