Some approximation results for Stancu type Lupaş–Schurer operators based on (p, q)-integers

Kanat K., Sofyalıoğlu M.

Applied Mathematics and Computation, vol.317, pp.129-142, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 317
  • Publication Date: 2018
  • Doi Number: 10.1016/j.amc.2017.08.046
  • Journal Name: Applied Mathematics and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.129-142
  • Keywords: (p, q)-integers, Functions of Lipschitz class, Korovkin type approximation theorem, Lupaş operators, Modulus of continuity, Peetre's K-functionals
  • Ankara Haci Bayram Veli University Affiliated: No

Abstract

In the present paper, we introduce the Stancu type generalisation of Lupaş–Schurer operators based on (p, q)-integers. We are concerned with the basic convergence of the constructed operators based on Korovkin's type approximation theorem. Further, we obtain the rate of convergence for the new operators in terms of the modulus of continuity, with the help of functions of Lipschitz class and Peetre's K-functionals. Then, we present three significant numerical mathematical algorithms. Finally, in order to confirm our theoretical results we obtain error estimation and illustrate the convergence of the (p, q)-Lupaş–Schurer–Stancu operators to certain functions by using MATLAB.