A modification of Bernstein-Durrmeyer operators with Jacobi weights on the unit interval (Q6601632)

In this research, the authors studied a sequence of positive linear operators that acts on the class of all continuous functions on \([0,1]\) as well as on some weighted spaces of integrable functions on \([0,1].\) The operators they explored are a generalization of the Bernstein-Durrmeyer operators having Jacobi weights. They established the qualitative and approximation properties of these operators and estimated their rate of convergence. Further, they compared the defined operator with the Bernstein-Durrmeyer and their modifications by using the asymptotic formula. In the end, they studied that in suitable intervals, the defined operators provide lower approximating error estimates.\N\NFor the entire collection see [Zbl 1515.46001].