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Approximation degree of a Kantorovich variant of Stancu operators based on Polya–Eggenberger distribution

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

This paper is a continuation of the work done by Deo et al. (Appl. Math. Comput. 273, 281–289, 2016), in which the authors have established some approximation properties of the Stancu–Kantorovich operators based on Pólya–Eggenberger distribution. We obtain some direct results for these operators by means of the Lipschitz class function, the modulus of continuity and the weighted space. Also, we study an approximation theorem with the aid of the unified Ditzian–Totik modulus of smoothness \(\omega _{\phi ^{\tau }}(f;t),\,\,\,0\le \tau \le 1\) and the rate of convergence of the operators for the functions having a derivative which is locally of bounded variation on \([0,\infty )\).

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Acknowledgements

The work of the second author was financed from Lucian Blaga University of Sibiu research Grants LBUS-IRG-2017-03 and the third author is thankful to “The Ministry of Human Resource and Development”, India for the 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 & Manjari Sidharth

  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. P. N. Agrawal
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  2. Ana Maria Acu
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  3. Manjari Sidharth
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Correspondence to Ana Maria Acu.

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Agrawal, P.N., Acu, A.M. & Sidharth, M. Approximation degree of a Kantorovich variant of Stancu operators based on Polya–Eggenberger distribution. RACSAM 113, 137–156 (2019). https://doi.org/10.1007/s13398-017-0461-0

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  • DOI: https://doi.org/10.1007/s13398-017-0461-0

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