Research article

Approximation by the modified $ \lambda $-Bernstein-polynomial in terms of basis function

  • Received: 29 August 2023 Revised: 04 January 2024 Accepted: 08 January 2024 Published: 18 January 2024
  • MSC : 33C45, 41A25, 41A36

  • In this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin's theorem, establish a local approximation theorem, and provide a convergence theorem for Lipschitz continuous functions and Peetre's $ K $-functional. In addition, we also obtain an asymptotic formula of the type Voronovskaja.

    Citation: Mohammad Ayman-Mursaleen, Md. Nasiruzzaman, Nadeem Rao, Mohammad Dilshad, Kottakkaran Sooppy Nisar. Approximation by the modified $ \lambda $-Bernstein-polynomial in terms of basis function[J]. AIMS Mathematics, 2024, 9(2): 4409-4426. doi: 10.3934/math.2024217

    Related Papers:

  • In this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin's theorem, establish a local approximation theorem, and provide a convergence theorem for Lipschitz continuous functions and Peetre's $ K $-functional. In addition, we also obtain an asymptotic formula of the type Voronovskaja.



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