Convergence analysis of max-product and max-min Durrmeyer-type exponential sampling operators in Mellin Orlicz space

TL;DR

This paper investigates the convergence properties of max-product and max-min Durrmeyer-type exponential sampling operators within Mellin Orlicz spaces, providing theoretical proofs and numerical illustrations of their approximation capabilities.

Contribution

It offers new convergence results for these operators in Mellin Orlicz spaces, including pointwise, uniform, and modular convergence, along with numerical analysis.

Findings

Established pointwise and uniform convergence in specific function spaces

Demonstrated modular convergence in Orlicz spaces

Provided numerical examples illustrating convergence rates

Abstract

In the present study, we establish both pointwise and uniform convergence in the space of logarithmically uniformly continuous and bounded functions for the max-product and max-min Durrmeyer-type exponential sampling operators. Furthermore, the modular convergence of these operators is demonstrated within the framework of Orlicz space. In addition to the theoretical results, we provide numerical and graphical analyses for various kernel pairs, illustrating the convergence rates and approximation behavior of the proposed operators.