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Approximation by \(\vartheta \)-Baskakov–Durrmeyer-Type Hybrid Operators

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Abstract

In this work, we present a Durrmeyer-type operator having the basis functions in summation and integration due to Aral (Math Commun 24:119–131, 2019) and Pǎltǎnea (Carpath J Math 24(3):378–385, 2008) that preserve the constant functions. We compute the rate of convergence of these operators in a weighted space and also computed a quantitative Voronovskaja-type asymptotic formula as well as a Grüss-Voronovskaya-type approximation.

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Authors and Affiliations

  1. School of Basic Sciences, Central University of Haryana, Haryana, 123031, India

    Arun Kajla

  2. Department of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Syed Abdul Mohiuddine

  3. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    Syed Abdul Mohiuddine & Abdullah Alotaibi

  4. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, 147004, India

    Meenu Goyal

  5. Department of Applied Science and Humanities, Institute of Engineering and Technology, Sitapur Road, Lucknow, Uttar Pradesh, 226021, India

    Karunesh Kumar Singh

Authors
  1. Arun Kajla
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  2. Syed Abdul Mohiuddine
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  3. Abdullah Alotaibi
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  4. Meenu Goyal
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  5. Karunesh Kumar Singh
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Correspondence to Arun Kajla.

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Kajla, A., Mohiuddine, S.A., Alotaibi, A. et al. Approximation by \(\vartheta \)-Baskakov–Durrmeyer-Type Hybrid Operators. Iran J Sci Technol Trans Sci 44, 1111–1118 (2020). https://doi.org/10.1007/s40995-020-00914-3

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  • DOI: https://doi.org/10.1007/s40995-020-00914-3

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