Convergence properties of Durrmeyer-type sampling operators (Q6616170)

The authors study the approximation properties of Durrmeyer-type sampling operators. They consider the composition of generalized sampling operators and Durrmeyer sampling operators. For the newly composed operators, they establishe the pointwise convergence, uniform convergence, and quantitative estimates using the usual modulus of continuity and \(K\)-functional. Further, they investigate the convergence rate using weighted modulus and provided difference estimates for the operators. The approximation results for the linear combinations of the composition operators are also studied. In the end, they graphically discuss the convergence rate of the operators.