### Direct estimates of certain Miheşan-Durrmeyer type operators

Arun Kajla

#### Abstract

In this note we consider a Durrmeyer type operator having the basis functions in summation and integration due to Mihecşan [Creative Math. Inf. 17 (2008), 466-472.] and Pvǎltvǎnea [Carpathian J. Math. 24 (2008), no. 3, 378-385.] that preserve the linear functions. We present a Voronovskaja type theorem, local approximation theorem by means of second order modulus of continuity and weighted approximation for these operators. In the last section of the paper, we obtain the rate of approximation for absolutely continuous functions having a derivative equivalent with a function of bounded variation.

#### Article information

Source
Adv. Oper. Theory Volume 2, Number 2 (2017), 162-178.

Dates
Accepted: 28 February 2017
First available in Project Euclid: 4 December 2017

https://projecteuclid.org/euclid.aot/1512431563

Digital Object Identifier
doi:10.22034/aot.1612-1079

Zentralblatt MATH identifier
06711475

#### Citation

Kajla, Arun. Direct estimates of certain Miheşan-Durrmeyer type operators. Adv. Oper. Theory 2 (2017), no. 2, 162--178. doi:10.22034/aot.1612-1079. https://projecteuclid.org/euclid.aot/1512431563

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