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On Shape Parameter α‐Based Approximation Properties and q‐Statistical Convergence of Baskakov‐Gamma Operators

Author

Listed:
  • Ming-Yu Chen
  • Md Nasiruzzaman
  • Mohammad Ayman Mursaleen
  • Nadeem Rao
  • Adem Kilicman

Abstract

We construct a novel family of summation‐integral‐type hybrid operators in terms of shape parameter α ∈ [0,1] in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre’s K‐functional, Lipschitz class, and second‐order modulus of smoothness. The approximation results are then obtained in weighted space. Finally, for these operators q‐statistical convergence is also investigated.

Suggested Citation

  • Ming-Yu Chen & Md Nasiruzzaman & Mohammad Ayman Mursaleen & Nadeem Rao & Adem Kilicman, 2022. "On Shape Parameter α‐Based Approximation Properties and q‐Statistical Convergence of Baskakov‐Gamma Operators," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4190732
    DOI: 10.1155/2022/4190732
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    References listed on IDEAS

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    1. Adem Kilicman & Mohammad Ayman Mursaleen & Ahmed Ahmed Hussin Ali Al-Abied, 2020. "Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties," Mathematics, MDPI, vol. 8(7), pages 1-13, July.
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