Approximation by (p, q) -Lupaş–Schurer–Kantorovich operators

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Kanat K., Sofyalıoğlu M.

Journal of Inequalities and Applications, vol.2018, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2018
  • Publication Date: 2018
  • Doi Number: 10.1186/s13660-018-1858-9
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: (p, q) -integers, Korovkin’s approximation theorem, Local approximation, Lupaş operators, Rate of convergence
  • Ankara Haci Bayram Veli University Affiliated: Yes

Abstract

In the current paper, we examine the (p, q) -analogue of Kantorovich type Lupaş–Schurer operators with the help of (p, q) -Jackson integral. Then, we estimate the rate of convergence for the constructed operators by using the modulus of continuity in terms of a Lipschitz class function and by means of Peetre’s K-functionals based on Korovkin theorem. Moreover, we illustrate the approximation of the (p, q) -Lupaş–Schurer–Kantorovich operators to appointed functions by the help of Matlab algorithm and then show the comparison of the convergence of these operators with Lupaş–Schurer operators based on (p, q) -integers.