Work

ANN-Assisted Sharp Bounds for Higher-Order Euler–Maclaurin Inequalities

Year: 2026

Type: article

Abstract: This study presents some novel sharp estimates of the Euler–Maclaurin inequality using a new higher-order derivative Maclaurin identity. By utilizing the properties of convexity and classical inequalities, we exploit various novel tight boundaries of the Euler–Maclaurin inequality. They offer alternatives to measuring the sharp bounds of the mean integral of the higher-order differentiable mappings. In order to prove the importance and precision of the key findings, we apply graphical and numerical techniques. Another important section evaluates the behavior and validity of inequalities using a neural network model. The method is not only utilized to authenticate the results but also brings out the practical advancements of the study within a computational framework. The method and results of the article provide an insight and develop a solid connection between inequalities, higher-order derivative convex mappings, numerical analysis, approximation theory, and artificial neural networking.

Source: Axioms

DOI: 10.3390/axioms15050358

Authors: Muhammad Zakria Javed, Muhammad Uzair Awan, Loredana Ciurdariu, Eugenia Grecu, Hala Mostafa

Institutions: Government College University, Faisalabad, Politehnica University of Timisoara, Princess Nourah bint Abdulrahman University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Princess Nourah Bint Abdulrahman University