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.