On the approximation by operators of Bernstein–Stancu types

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Recently, Gadjiev and Ghorbanalizadeh (2010) introduced a new type of generalized Bernstein–Stancu polynomials, and obtained a direct result (see Gadjiev and Ghorbanalizadeh, 2010, Theorem 2). In the present paper, we obtain both the direct result and the inverse result of approximation by the polynomials. Our results are pointwise. Furthermore, we also consider the approximation by a type of more generalized Bernstein–Stancu operators introduced by Taşdelen et al. (2012) for functions of smoothness.