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Approximation by Generalized Lupaş Operators Based on q -Integers

Author

Listed:
  • Mohd Qasim

    (Department of Mathematical Sciences, Baba Ghulam Shah Badshah University, Rajouri 185234, Jammu and Kashmir, India)

  • M. Mursaleen

    (Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40402, Taiwan
    Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
    Department of Computer Science and Information Engineering, Asia University, Taichung 41354, Taiwan)

  • Asif Khan

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Zaheer Abbas

    (Department of Mathematical Sciences, Baba Ghulam Shah Badshah University, Rajouri 185234, Jammu and Kashmir, India)

Abstract

The purpose of this paper is to introduce q -analogues of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing, and unbounded function ρ . Depending on the selection of q , these operators provide more flexibility in approximation and the convergence is at least as fast as the generalized Lupaş operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation.

Suggested Citation

  • Mohd Qasim & M. Mursaleen & Asif Khan & Zaheer Abbas, 2020. "Approximation by Generalized Lupaş Operators Based on q -Integers," Mathematics, MDPI, vol. 8(1), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:68-:d:304647
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    References listed on IDEAS

    as
    1. N. I. Mahmudov, 2012. "Approximation by the -Szász-Mirakjan Operators," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, December.
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    1. Ahasan, Mohd. & Mursaleen, M., 2020. "Generalized Szász-Mirakjan type operators via q-calculus and approximation properties," Applied Mathematics and Computation, Elsevier, vol. 371(C).

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