Multivariate approximation in phi-variation for nonlinear integral operators via summability methods

ASLAN İ.

TURKISH JOURNAL OF MATHEMATICS, vol.46, pp.277-298, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 46
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2109-77
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.277-298
  • Keywords: Convolution type operators, N-dimensional nonlinear integral operators, bounded &phi, -variation, summa-bility process, order of approximation, DISCRETE OPERATORS, SAMPLING-TYPE, CONVERGENCE
  • Hacettepe University Affiliated: Yes

Abstract

We consider convolution-type nonlinear integral operators endowed with Musielak-Orlicz yo-variation. Our aim is to get more powerful approximation results with the help of summability methods. In this study, we use yo absolutely continuous functions for our convergence results. Moreover, we study the order of approximation using suitable Lipschitz class of continuous functions. A general characterization theorem for yo-absolutely continuous functions is also obtained. We also give some examples of kernels in order to verify our approximations. At the end, we indicate our approximations in figures together with some numerical computations.