A New Type of Bivariate λ‐Bernstein Operators With Three Shape Parameters on Triangular Domains

ABSTRACT This article introduces a novel class of bivariate ‐Bernstein operators, denoted as , defined on a triangular domain, constructed using a new class of bivariate Bézier basis functions characterized by shape parameters , , and . A Korovkin‐type approximation theorem is proved for , with its convergence rate described in terms of the complete modulus of continuity and the partial moduli of continuity. Furthermore, a local approximation theorem and a Voronovskaja‐type asymptotic formula are derived. Finally, the convergence of to is demonstrated through graphical and numerical illustrations. The numerical examples illustrate the convergence behavior of and show that the additional shape parameter may provide greater flexibility in approximation on the triangular domain.