Blending type approximation by GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type

Abstract

Abstract In this paper, we introduce a family of GBS $GBS$ operators of bivariate tensor product of λ-Bernstein–Kantorovich type. We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja type asymptotic formula for the bivariate λ-Bernstein–Kantorovich operators, as well as give some examples and their graphs to show the effect of convergence.

Keywords

• B-continuous functions
• B-differentiable functions
• G B S $GBS$ operators
• Bernstein–Kantorovich operators
• Mixed modulus of smoothness