Acar, TuncerAcu, Ana-MariaManav, Nesibe2020-03-262020-03-2620181846-579Xhttps://dx.doi.org/10.7153/jmi-2018-12-74https://hdl.handle.net/20.500.12395/36345Very 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.en10.7153/jmi-2018-12-74info:eu-repo/semantics/openAccessGenuine Bernstein-Durrmeyer operatorsRate of convergenceLinear positive operatorsArticle124975987WOS:000451334900007Q1