Approximation properties of <italic>λ</italic>-Bernstein operators.

In this paper, we introduce a new type <italic>λ</italic>-Bernstein operators with parameter λ∈[−1,1]<inline-graphic></inline-graphic>, 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 Bn,λ(f;x)<inline-graphic></inline-graphic> to f(x)<inline-graphic></inline-graphic>, and we see that in some cases the errors are smaller than Bn(f)<inline-graphic></inline-graphic> to <italic>f</italic>. [ABSTRACT FROM AUTHOR]