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    Approximation of Functions by Genuine Bernstein-Durrmeyer Type Operators
    (ELEMENT, 2018) Acar, Tuncer; Acu, Ana-Maria; Manav, Nesibe
    Very recently, in [4] Chen et. al introduced and considered a new generalization of Bernstein polynomials depending on a patameter alpha. As classical Bernstein operators, these operators also provide interpolation at the end points of [0,1] and they have the linear precision property which means those reproduce the linear functions. In this paper we introduce genuine alpha-Bernstein-Durrmeyer operators. Some approximation results, which include local approximation, error estimation in terms of Ditzian-Totik modulus of smoothness are obtained. Also, the convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.
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    Some approximation properties by a class of bivariate operators
    (WILEY, 2019) Acu, Ana-Maria; Acar, Tuncer; Muraru, Carmen-Violeta; Radu, Voichita Adriana
    Starting with the well-known Bernstein operators, in the present paper, we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely, the generalized Boolean sum (GBS) in the Bogel space of continuous functions is given. In order to underline the fact that in this particular case, GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also, the error of approximation for the modified Bernstein operators and its GBS-type operator are compared.