Approximation properties of λ-Bernstein operators.

In this paper, we introduce a new type λ-Bernstein operators with parameter [Formula: see text], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of [Formula: see text] to [Formula: see text], and we see that in some cases the errors are smaller than [Formula: see text] to f.