Approximation Properties of Mellin-Steklov Type Exponential Sampling Series

TL;DR

This paper introduces Mellin-Steklov exponential sampling operators, analyzes their approximation capabilities in various function spaces, and establishes convergence and error estimates with practical examples.

Contribution

It presents a new class of Mellin-Steklov exponential sampling operators and studies their approximation properties and convergence in different function spaces.

Findings

High order of approximation achieved using the operators.

Established a Voronovskaja type theorem for the operators.

Provided examples of kernels supporting the theoretical results.

Abstract

In this paper, we introduce Mellin-Steklov exponential samplingoperators of order $r,r\in\mathbb{N}$, by considering appropriate Mellin-Steklov integrals. We investigate the approximation properties of these operators in continuousbounded spaces and $L^p, 1 \leq p < \infty$ spaces on $\mathbb{R}_+.$ By using the suitablemodulus of smoothness, it is given high order of approximation. Further, we present a quantitative Voronovskaja type theorem and we study the convergence results of newly constructed operators in logarithmic weighted spaces offunctions. Finally, the paper provides some examples of kernels that support the our results.