Approximation by λ-Bernstein type operators on triangular domain

( ) ( ) Abstract. In this paper, a new type of lambda-Bernstein operators Bwm,lambda g(w, z) and Bz )n,lambda g(w, z), their Products ( ( ) ( ) ( ) Pmn,lambda g(w, z), Qnm,lambda g(w, z), and their Boolean sums Smn,lambda g(w, z), Tnm,lambda g(w, z) are constructed on trian-gle Rh with parameter lambda is an element of [-1, 1]. Convergence theorem for Lipschitz type continuous functions and a Voronovskaja-type asymptotic formula are studied for these operators. Remainder terms for error evalua-tion 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 do-main. Also, we show that the parameter lambda will provide flexibility in approximation; in some cases, the approximation will be better than its classical analogue.