Approximation by λ-Bernstein type operators on triangular domain

Abstract

In this paper, a new type of ?-Bernstein operators (Bwm,?g)(w,z) and (Bzn ?g)(w,z), their Products Pmn,?g (w,z), Qnm,?g (w, z), and their Boolean sums Smn,?g (w,z), Tnm,?g (w, z) are constructed on triangle h with parameter ? [1,1]. Convergence theorem for Lipschitz type continuous functions and a Voronovskaja-type asymptotic formula are studied for these operators. Remainder terms for error evaluation by using the modulus of continuity are discussed. Graphical representations are added to demonstrate the consistency of theoretical findings for the operators approximating functions on the triangular domain. Also, we show that the parameter ? will provide flexibility in approximation; in some cases, the approximation will be better than its classical analogue.