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 B\’ezier variant of the operators D_n^M,1(f,x) is obtained.