APPROXIMATION PROPERTIES OF RIEMANN-LIOUVILLE TYPE FRACTIONAL BERNSTEIN-KANTOROVICH OPERATORS OF ORDER α

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Baytunç E., Aktuglu H., Mahmudov N.

Mathematical Foundations of Computing, vol.7, no.4, pp.544-567, 2024 (ESCI) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 7 Say: 4
  • Nəşr tarixi: 2024
  • Doi nömrəsi: 10.3934/mfc.2023030
  • jurnalın adı: Mathematical Foundations of Computing
  • Jurnalın baxıldığı indekslər: Emerging Sources Citation Index (ESCI), Scopus
  • Səhifə sayı: pp.544-567
  • Açar sözlər: affine functions, Bernstein-Kantorovich operators, bivariate Bernstein-Kantorovich operators, modulus of continuity, positive linear operators, rate of convergence
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

In this paper, we construct a new sequence of Riemann-Liouville type fractional Bernstein-Kantorovich operators Knα(f; x) depending on a parameter α. We prove a Korovkin type approximation theorem and discuss the rate of convergence with the first and second order modulus of continuity of these operators. Moreover, we introduce a new operator that preserves affine functions from Riemann-Liouville type fractional Bernstein-Kantorovich operators. Further, we define the bivariate case of Riemann-Liouville type fractional Bernstein-Kantorovich operators and investigate the order of convergence. Some numerical results are given to illustrate the convergence of these operators and its comparison with the classical case of these operators.