Open Access
Spring 2017 Direct estimates of certain Miheşan-Durrmeyer type operators
Arun Kajla
Adv. Oper. Theory 2(2): 162-178 (Spring 2017). DOI: 10.22034/aot.1612-1079


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.


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Arun Kajla. "Direct estimates of certain Miheşan-Durrmeyer type operators." Adv. Oper. Theory 2 (2) 162 - 178, Spring 2017.


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

zbMATH: 06711475
MathSciNet: MR3730066
Digital Object Identifier: 10.22034/aot.1612-1079

Primary: 26A15
Secondary: 41A25 , 41A28

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

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.2 • No. 2 • Spring 2017
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