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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.

MSC:

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