Degree of Approximation by Certain Durrmeyer Type Operators
DOI:
https://doi.org/10.5890/DNC.2022.06.006Abstract
We obtain local and global rate of approximation by two new variants, $D_n^{M,1}(f,x)$ and $D_n^{M,2}(f,x)$ of Bernstein Durrmeyer operators, recently introduced by Acu et al. By utilizing a suitable Ditzian-Totik modulus of smoothness, we prove that the approximation process $D_n^{M,2}(f,x)$ is quadratic convergent. An error estimate for the functions of bounded variation by the B\'{e}zier variant of the operators $D_n^{M,1}(f,x)$ is obtained.References
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