We consider the question if lower estimates in terms of the second order Ditzian-Totik modulus are possible, when we measure the pointwise approximation of continuous function by Bernstein operator.â€¦ (More)

In this work we discuss the rate of simultaneous approximation of HÃ¶lder continuous functions by Bernstein operators, measured by HÃ¶lder norms with different exponents. We extend the known results onâ€¦ (More)

In the present article we establish pointwise variant of E. V. Voronovskajaâ€™s 1932 result, concerning the degree of approximation of Bernstein operator, applied to functions fâ€‰âˆˆâ€‰C 3[0, 1].

The aim of this note is to study the magnitude of the constants in the equivalence between the first and second order Ditzian-Totik moduli of smoothness and related K-functionals. Applications toâ€¦ (More)

For pointwise approximation of bounded continuous functions by linear combinations of Phillips operators we represent equivalent relation by means of Ditzian-Totik modulus of smoothness. The rate ofâ€¦ (More)