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P-summability method applied to multivariate (p, q)-Lagrange polynomial operators

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Abstract

The present work introduces a (p, q)-analogue of a linear positive operator based on multivariate Lagrange polynomials (Erkuş et al. in Appl Math Comput 182:213–222, 2006). Using P-summability convergence technique, we state and prove a non-trivial Korovkin type approximation theorem. Also, we provide a generalization of the proposed operator in response to the smoothness of a function and see the approximation behavior of a sufficiently smooth members of the Lipschitz class.

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Acknowledgements

The authors are indebted to the anonymous reviewer(s) for the fruitful suggestions. We strongly believe, the comments has greatly improved the overall structure of the article. The first author is highly grateful to a lovely person who was the continuous source of his happiness, Mr. Gentleman AKA Chattu. Mr. Gentleman was his pup in PhD’s days, and supported the first author emotionally during the unprecedented pandemic. Unfortunately, our Gentleman is on the journey to infinity now!

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Authors and Affiliations

  1. Department of Mathematics, Deshbandhu College, University of Delhi, New Delhi, India

    Rahul Shukla

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    Purshottam Narain Agrawal

  3. Department of Mathematics, University of Prishtina, Prishtina, Kosovo

    Behar Baxhaku

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  1. Rahul Shukla
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  2. Purshottam Narain Agrawal
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  3. Behar Baxhaku
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All the authors have equally contributed to the conceptualization, framing and writing of the manuscript.

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Correspondence to Rahul Shukla.

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Shukla, R., Agrawal, P.N. & Baxhaku, B. P-summability method applied to multivariate (p, q)-Lagrange polynomial operators. Anal.Math.Phys. 12, 148 (2022). https://doi.org/10.1007/s13324-022-00757-8

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  • DOI: https://doi.org/10.1007/s13324-022-00757-8

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