On Bivariate Kantorovich Exponential Sampling Series

TL;DR

This paper investigates the approximation capabilities of bivariate Kantorovich exponential sampling series, providing theoretical results, convergence estimates, and practical examples with graphical illustrations.

Contribution

It introduces a bivariate generalization of Kantorovich exponential sampling series and derives new approximation theorems, including Voronovskaya and quantitative convergence estimates.

Findings

Established point-wise and Voronovskaya type theorems.

Derived order of convergence using modulus of smoothness.

Provided examples with kernels and graphical error analysis.

Abstract

We analyse the approximation properties of the bivariate generalization of the family of Kantorovich type exponential sampling series. We derive the point-wise and Voronovskaya type theorem for these sampling type series. Using the modulus of smoothness, we obtain the quantitative estimate of order of convergence of these series. Further, we establish the degree of approximation for these series associated with generalized Boolean sum (GBS) operators. Finally, we provide a few examples of kernels to which the theory can be applied along with the graphical representation and error estimates.