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Bezier variant of the Bernstein-Durrmeyer type operators
(Springer Basel Ag, 2017) Acar, Tuncer; Agrawal, P. N.; Neer, Trapti
In the present paper, we introduce the Bezier-variant of Durrmeyer modification of the Bernstein operators based on a function , which is infinite times continuously differentiable and strictly increasing function on [0, 1] such that and . We give the rate of approximation of these operators in terms of usual modulus of continuity and K-functional. Next, we establish the quantitative Voronovskaja type theorem. In the last section we obtain the rate of convergence for functions having derivative of bounded variation.