Year: 2025
Type: article
Abstract: Recent results have provided important functional generalizations, extensions and improvements of the Hardy and Levinson integral inequalities. However, they require some assumptions on the main functions, such as monotonicity or convexity assumptions, which remain somewhat restrictive. In this article, we propose two new ideas of functional generalizations, one based on a series expansion approach and the other on an integral approach. Both achieve the goal of offering adaptable generalizations and extensions of the Hardy and Levinson integral inequalities. They are formulated in two different general theorems, which are proved in detail. Several examples of new integral inequalities are derived.
Source: Mathematica Pannonica
Author: Christophe Chesneau
Institution: Université de Caen Normandie
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409440256