Bézier–Bernstein–Durrmeyer type operators
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In this note, we construct the Bézier variant of the Bernstein–Durrmeyer type operators. We present local results, a direct approximation theorem by using the Ditzian–Totik modulus of smoothness and a quantitative Voronovskaja type theorem with the help of the Ditzian–Totik modulus of continuity. The rate of convergence for differential functions whose derivatives are of bounded variation is also established. Finally, we show that the numerical examples which illustrate the authenticity of the theoretical results and the effectiveness of the defined operators.
KeywordsPositive approximation process Bézier operators Degree of approximation
Mathematics Subject Classification41A25 26A15
The second author has been partially supported within TUBITAK (The Scientific and Technological Research Council of Turkey) 1002-Project 119F191.
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