Pointwise Approximation for Linear Combinations of Bernstein Operators

For linear combinations of Bernstein operators Bn, r(f, x), we give an equivalent theorem with ω2rφλ(f, t), where ω2rφλ(f, t) is the Ditzian–Totik modulus of smoothness (1−1/rλ1). It is the generalization of corresponding results by Z. Ditzian and V. Totik (1987, “Moduli of Smoothness”, Springer-Verlag, Berlin/New York).