Approximation by generalized bivariate Kantorovich sampling type series

TL;DR

This paper introduces a bivariate generalization of Kantorovich sampling operators, proving convergence, approximation rates, and applying the theory to specific kernels like box splines and Bochner-Riesz.

Contribution

It develops a new bivariate Kantorovich sampling series with convergence and approximation theorems, extending existing univariate results.

Findings

Pointwise convergence of the series

Quantitative approximation estimates

Applicability to specific kernels like box splines

Abstract

The purpose of this paper is to construct a bivariate generalization of new family of Kantorovich type sampling operators $(K_w^{\varphi}f)_{w>0}.$ First, we give the pointwise convergence theorem and a Voronovskaja type theorem for these Kantorovich generalized sampling series. Further, we obtain the degree of approximation by means of modulus of continuity and quantitative version of Voronovskaja type theorem for the family $(K_w^{\varphi}f)_{w>0}.$ Finally, we give some examples of kernels such as box spline kernels and Bochner-Riesz kernel to which the theory can be applied.