Lupaş type Bernstein operators on triangles based on quantum analogue

Abstract

The purpose of the paper is to introduce new analogues of Lupaş type Bernstein operators Bm,quf(u,v) and Bn,qvf(u,v), their products Pmn,qf(u,v) and Qnm,qf(u,v) and their Boolean sums Smn,qf(u,v) and Tnm,qf(u,v)on triangle Th, which interpolate a given function on the some edges and at the vertices of triangle using quantum analogue. Based on Peano’s theorem and using modulus of continuity, the remainders of the approximation formula of corresponding operators are evaluated. It has been shown that parameter q will provide more flexibility for approximation.

Keywords

• Lupaş q-Bernstein operators
• Product operators
• Boolean sum operators
• Modulus of continuity
• Peano’s theorem
• Error estimation