Direct and inverse results for Kantorovich type exponential sampling series

TL;DR

This paper investigates the properties of Kantorovich type exponential sampling series, establishing approximation theorems, inverse results, and providing practical examples and visualizations for these operators.

Contribution

It introduces new theoretical results for Kantorovich exponential sampling series, including point-wise approximation, Voronovskaya theorem, and inverse approximation formulas.

Findings

Established point-wise approximation theorem

Proved Voronovskaya type theorem

Provided examples and graphical illustrations

Abstract

In this article, we analyze the behaviour of the new family of Kantorovich type exponential sampling series. We obtain the point-wise approxi mation theorem and Voronovskaya type theorem for the series. Further, we obtain a representation formula and an inverse result approximation for these operators. Finally, we give some examples of kernel functions to which the theory can be applied along with the graphical representation.