# Inverse approximation and GBS of bivariate Kantorovich type sampling series

## TL;DR

This paper establishes inverse approximation results for bivariate Kantorovich sampling series, analyzes their approximation rates in specific function spaces, and provides practical kernel examples for application.

## Contribution

It introduces inverse theorems and approximation rate analysis for bivariate Kantorovich sampling series, extending the theoretical understanding of these operators.

## Key findings

- Inverse approximation results for bivariate Kantorovich series
- Rate of approximation in Bogel space for GBS operators
- Examples of kernels applicable to the theory

## Abstract

In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for the space of all continuous functions with upto second order partial derivatives are continuous and bounded on $R^2.$ Further, we prove the rate of approximation in the Bogel space of continuous functions for the GBS (Generalized Boolean Sum) of these operators. Finally, we give some examples for the kernel to which the theory can be applied