Advances in Operator Theory

Direct estimates of certain Miheşan-Durrmeyer type operators

Arun Kajla

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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
Received: 12 December 2016
Accepted: 28 February 2017
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431563

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

Zentralblatt MATH identifier
06711475

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
Secondary: 41A25: Rate of convergence, degree of approximation 41A28: Simultaneous approximation

Keywords
positive approximation process rate of convergence modulus of continuity Steklov mean

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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