Bernstein–Schurer–Kantorovich operators based on q-integers

P.N. Agrawal, Zoltán Finta and A. Sathish Kumar

Applied Mathematics and Computation, 2015, vol. 256, issue C, 222-231

Abstract: In this paper, we introduce a new Kantorovich type generalization of the q-Bernstein–Schurer operators defined in Muraru (2011). First, we give the basic convergence theorem and then obtain the local direct results for these operators, estimating the rate of convergence by using the modulus of smoothness and the Lipschitz type maximal function, respectively. We also obtain a Voronovskaja type theorem and investigate the statistical approximation properties of these operators with the help of a Korovkin type statistical approximation theorem given in Duman (2008).

Keywords: q-Bernstein–Schurer–Kantorovich operators; q-Integers; Rate of convergence; Modulus of smoothness; Lipschitz type maximal function; A-statistical convergence (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:256:y:2015:i:c:p:222-231

DOI: 10.1016/j.amc.2014.12.106

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