On certain Durrmeyer type operators. (English) Zbl 1183.41012

Summary: N. Deo [Appl. Math. Comput. 204, No. 1, 109–115 (2008; Zbl 1181.41040)] introduced \(n\)-th Durrmeyer operators defined for functions integrable in some interval \(I\). There are gaps and mistakes in some of his lemmas and theorems. Further, in his paper [Mat. Vesn. 58, No. 1–2, 19–29 (2006; Zbl 1119.41017)] he did not give results on simultaneous approximation as the title reveals. The purpose of this paper is to correct those mistakes.


41A25 Rate of convergence, degree of approximation
41A30 Approximation by other special function classes