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