Weighted Approximation By Max-Product Generalized Exponential Sampling Series

TL;DR

This paper investigates the convergence properties of the generalized Max Product exponential sampling series in weighted spaces, providing both basic and asymptotic convergence results along with quantitative approximation estimates.

Contribution

It introduces new convergence analysis for the series in weighted spaces and derives quantitative approximation bounds using weighted logarithmic modulus of continuity.

Findings

Convergence of the series in weighted spaces established.

Asymptotic convergence behaviour analyzed.

Quantitative approximation results obtained.

Abstract

In this article, we study the convergence behaviour of the classical generalized Max Product exponential sampling series in the weighted space of log-uniformly continuous and bounded functions. We derive basic convergence results for both the series and study the asymptotic convergence behaviour. Some quantitative approximation results have been obtained utilizing the notion of weighted logarithmic modulus of continuity.