Some inequalities of trigonometric approximation in weighted Orlicz spaces

In the present work, we proved a refined direct theorem and an exact inverse theorem of trigonometric approximation in Orlicz spaces with weights satisfying some Muckenhoupt’s

Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights

Using the equivalence relation betweenK-functional and modulus of smoothness, we establish a strong direct theorem and an inverse theorem of weak type for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex in this paper. We also obtain a characterization for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex. The obtained results not only generalize the corresponding ones for Bernstein-Durrmeyer operators, but also give approximation order of Bernstein-Durrmeyer operators.