English

Approximation by generalized Kantorovich sampling type series

Classical Analysis and ODEs 2017-09-12 v1

Abstract

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators (Kwφf)w>0.(K_w^{\varphi}f)_{w>0}. First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a corresponding quantitative version in terms of the first order of modulus of continuity. Further, we study the order of approximation in C(R)C({\mathbb{R}}) (the set of all uniformly continuous and bounded functions on R{\mathbb{R}}) for the family (Kwφf)w>0.(K_w^{\varphi}f)_{w>0}. Finally, we give some examples of kernels such as B-spline kernels and Blackman-Harris kernel to which the theory can be applied.

Keywords

Cite

@article{arxiv.1709.03274,
  title  = {Approximation by generalized Kantorovich sampling type series},
  author = {A. Sathish Kumar and P. Devaraj},
  journal= {arXiv preprint arXiv:1709.03274},
  year   = {2017}
}
R2 v1 2026-06-22T21:38:45.390Z