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Kantorovich Variant of Ismail–May Operators

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Abstract

The prime objective of this paper is to construct the Kantorovich variant of Ismail–May operators depending on a non-negative parameter \(\lambda \). We estimate the rate of convergence of the proposed operators for functions in Lipschitz-type space. Further, an improved quantitative Voronovskaya-type estimate in terms of the second-order modulus of continuity and a direct approximation theorem using Ditzian–Totik modulus of smoothness is also given. The last section is dedicated to the bivariate generalisation of the proposed operators and estimation of their rate of convergence in terms of partial and total modulus of continuity and Peetre’s K-functional. A Voronovskaya-type result is also obtained. Finally, some graphs and error estimation table to illustrate the convergence of the proposed operators are presented using Mathematica software.

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Acknowledgements

The first author expresses her sincere thanks to Mr. Ram Pratap for his continued support and helpful discussions during the preparation of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, Shahbad Daulatpur, Main Bawana Road, Delhi, 110042, India

    Nav Shakti Mishra & Naokant Deo

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  1. Nav Shakti Mishra
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  2. Naokant Deo
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Correspondence to Nav Shakti Mishra.

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Mishra, N.S., Deo, N. Kantorovich Variant of Ismail–May Operators. Iran J Sci Technol Trans Sci 44, 739–748 (2020). https://doi.org/10.1007/s40995-020-00863-x

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  • DOI: https://doi.org/10.1007/s40995-020-00863-x

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