Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Direct and converse results for q-Bernstein operators

Zoltán Fintaa1

a1 Department of Mathematics, Babeş-Bolyai University, Mihail Kogălniceanu nr. 1, RO 400084, Cluj-Napoca, Romania; Email: (


Direct and converse theorems are established for the q-Bernstein polynomials introduced by G. M. Phillips. The direct approximation theorems are given for the second-order Ditzian–Totik modulus of smoothness. The converse results are theorems of Berens–Lorentz type.

(Received October 12 2007)


  • q-Bernstein polynomials;
  • K-functional;
  • Ditzian–Totik modulus of smoothness;
  • Berens–Lorentz-type theorem

2000 Mathematics subject classification

  • Primary 41A10;
  • 41A25;
  • 41A27;
  • 41A36