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Weighted approximation and GBS of Chlodowsky–Szász–Kantorovich type operators

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Abstract

The present paper deals with the approximation properties of the bivariate operators which are the combination of Bernstein–Chlodowsky operators and the Szász–Kantorovich type operators. We investigate the degree of approximation of the bivariate operators for continuous functions in the weighted space of polynomial growth. Further, we introduce the Generalized Boolean Sum (GBS) of these bivariate Chlodowsky–Szász–Kantorovich type operators and examine the order of approximation in the Bögel space of continuous functions by means of the Lipschitz class and mixed modulus of smoothness. Besides this, we compare the rate of convergence of the Chlodowsky–Szász–Kantorovich type operators and the associated GBS operators by numerical examples and tables using Maple algorithms. It turns out that the GBS operator converges faster to the function than the original operator.

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Acknowledgements

First author is very thankful to “The Ministry of Human Resource and Development, India” for the financial support to carry out her research work and the work of the second author was financed from Lucian Blaga University of Sibiu research Grants LBUS-IRG-2017-03.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Tarul Garg & P. N. Agrawal

  2. Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012, Sibiu, Romania

    Ana Maria Acu

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  1. Tarul Garg
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  2. Ana Maria Acu
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  3. P. N. Agrawal
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Correspondence to Ana Maria Acu.

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Garg, T., Acu, A.M. & Agrawal, P.N. Weighted approximation and GBS of Chlodowsky–Szász–Kantorovich type operators. Anal.Math.Phys. 9, 1429–1448 (2019). https://doi.org/10.1007/s13324-018-0246-4

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