Approximation by generalized Kantorovich sampling type series

TL;DR

This paper introduces and analyzes a new family of Kantorovich sampling operators, providing theoretical results on their approximation properties, including a Voronovskaya theorem and examples with specific kernels.

Contribution

It presents a novel family of Kantorovich sampling operators and establishes their approximation behavior with new theoretical results and practical kernel examples.

Findings

Established a Voronovskaya type theorem for the operators

Derived quantitative approximation estimates using modulus of continuity

Provided examples with B-spline and Blackman-Harris kernels

Abstract

In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators $(K_w^{\varphi}f)_{w>0}.$ 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 $C({\mathbb{R}})$ (the set of all uniformly continuous and bounded functions on ${\mathbb{R}}$) for the family $(K_w^{\varphi}f)_{w>0}.$ Finally, we give some examples of kernels such as B-spline kernels and Blackman-Harris kernel to which the theory can be applied.