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Approximation Properties by Modified Baskakov–Durrmeyer Operators Based on Shape Parameter-\(\alpha\)

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Abstract

In this research article, we construct a new sequence of Baskakov–Stancu–Durrmeyer operators including the shape parameter \(\alpha\) and study the uniform convergence of these operators by means of modulus of continuity to the continuous functions h(u) on \(u\in [0,1]\). We investigate the pointwise and weighted approximation in terms of Ditzian–Totik uniform with the aid of first and second order of modulus of smoothness. Further, we calculate the direct estimate of rate of convergence in terms of Lipschitz function. Next, we study weight approximation result.

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Acknowledgements

Authors are very grateful to the reviewers for their valuable suggestions and comments to the better presentation of this article.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Shree Guru Gobind Singh Tricentenary University, Gurugram, Haryana, 122505, India

    Nadeem Rao

  2. Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk, 71491, Saudi Arabia

    Md Nasiruzzaman

  3. Department of Natural And Applied Sciences, Glocal School of Science And Technology, Glocal University, Saharanpur, UP, 247121, India

    Md Heshamuddin & Mohd Shadab

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  1. Nadeem Rao
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  2. Md Nasiruzzaman
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  3. Md Heshamuddin
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  4. Mohd Shadab
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Correspondence to Nadeem Rao.

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Rao, N., Nasiruzzaman, M., Heshamuddin, M. et al. Approximation Properties by Modified Baskakov–Durrmeyer Operators Based on Shape Parameter-\(\alpha\). Iran J Sci Technol Trans Sci 45, 1457–1465 (2021). https://doi.org/10.1007/s40995-021-01125-0

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