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q-Analogue of a Kantorovitch Variant of an Operator Defined by Stancu

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Abstract

The purpose of this paper is to introduce a new kind of q −Stancu-Kantorovich type operators and study its various approximation properties. We establish some local direct theorems, e.g., Voronovskaja type asymptotic theorem, global approximation and an estimate of error by means of the Lipschitz type maximal function and the Peetre K-functional. We also consider a n th-order generalization of these operators and study its approximation properties. Next, we define a bivariate case of these operators and investigate the order of convergence by means of moduli of continuity and the elements of Lipschitz class. Furthermore, we consider the associated Generalized Boolean Sum (GBS) operators and examine the approximation degree for functions in a Bögel space. Some numerical examples to illustrate the convergence of these operators to certain functions are also given.

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Acknowledgements

The authors are extremely grateful to the learned reviewers for a critical reading of the manuscript and making valuable comments which improved the paper considerably. The third author is thankful to the Ministry of Human Resource and Development, Govt. of India for providing financial support to carry out the above work.

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Authors and Affiliations

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

    P. N. Agrawal & Abhishek Kumar

  2. Department of Mathematics, Central University of Haryana, Haryana, 123031, India

    Arun Kajla

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  1. P. N. Agrawal
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Correspondence to Arun Kajla.

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Agrawal, P., Kajla, A. & Kumar, A. q-Analogue of a Kantorovitch Variant of an Operator Defined by Stancu. Acta Math Vietnam 47, 781–816 (2022). https://doi.org/10.1007/s40306-021-00472-9

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