Degree of Approximation by Certain Durrmeyer Type Operators - Gairola, Asha Ram; Singh, Karunesh Kumar; Mishra, Lakshmi Narayan (Discontinuity, Nonlinearity, and Complexity, 2026)
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 Bézier variant of the operators $D_n^{M,1}(f,x)$ is obtained.