Approximation by Durrmeyer type Exponential Sampling Series

TL;DR

This paper investigates the approximation capabilities of a new family of Durrmeyer type exponential sampling operators, establishing their theoretical properties and demonstrating improved approximation through convex combinations and examples.

Contribution

The paper introduces a new family of Durrmeyer exponential sampling operators and analyzes their approximation properties, including point-wise, uniform, and Voronovskaya theorems, with enhanced results via convex combinations.

Findings

Derived point-wise and uniform approximation theorems.

Established Voronovskaya type theorem for the operators.

Constructed convex combinations yielding better approximation results.

Abstract

In this article, we analyze the approximation properties of the new family of Durrmeyer type exponential sampling operators. We derive the point-wise and uniform approximation theorem and Voronovskaya type theorem for these generalized family of operators. Further, we construct a convex type linear combination of these operators and establish the better approximation results. Finally, we provide few examples of the kernel functions to which the presented theory can be applied along with the graphical representation.