Lupas type Bernstein operators on triangles based on quantum analogue

The purpose of the paper is to introduce new analogues of Lupas type Bernstein operators (B-m,q(u) f) (u, v) and (B-n,q(u) f) (u, v), their products (P(mn,q)f) (u,v) and (Q(nm,q)f) (u, v) and their Boolean sums (S(mn,q)f) (u, v) and (T(nm,q)f) (u, v) on triangle T-h, 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. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.