Certain Approximation Results for Kantorovich Exponential Sampling Series

TL;DR

This paper investigates approximation properties of Kantorovich exponential sampling operators, establishing inverse theorems, saturation order, and relations to other sampling series for specific function classes.

Contribution

It introduces new inverse approximation results, saturation order, and links to generalized exponential sampling series for Kantorovich operators.

Findings

Established strong inverse approximation theorem.

Determined saturation order for the operators.

Provided examples of kernels satisfying the conditions.

Abstract

In this paper, we study a strong inverse approximation theorem and saturation order for the family of Kantorovich exponential sampling operators. The class of log-uniformly continuous and bounded functions, and class of log-H\"{o}lderian functions are considered to derive these results. We also prove some auxiliary results including Voronovskaya type theorem, and a relation between the Kantorovich exponential sampling series and the generalized exponential sampling series, to achieve the desired plan. Moreover, some examples of kernels satisfying the conditions, which are assumed in the hypotheses of our theorems, are discussed.