The q analogue of the limit case of bernstein type operators

Subject Analysis
Title The q analogue of the limit case of bernstein type operators
Author(s) Akif Barbaros Dikmen
Keywords bernstein type operators
Abstract In the present paper we introduce a q-analogue of the Bernstein-typeoperators which is de ned in citef4g. We estimate moments, establish direct theorems and rate of convergence in terms of themodulus of continuity. In 1997 Philips [1] proposed the following q-analogue of the well-known Bernstein polynomials,which for each positive integer n and f 2 C [0; 1] ;are de ned as, Bn;q (f; x) = Xn k=0 f  [k] [n]  pnk (q; x) : After Philips several researchers have studied convergence properties of q-Bernstein polynomials Bn;q (f; x) : We can refer to readers these important searchs in [12; 13; 14; 15] : P.E. Parvanov , B. D. Popov in 1994 mention Bernstein type operators and examined direct theo- rems and Jackson type inequality and some approximation properties. This motives us to examine and introduce q analogue of Bernstein type operators.