Year: 2024
Type: article
Abstract: The focus of this article is a Hardy-type integral inequality published in 2012, which has the particularity of combining convexity and submultiplicativity assumptions. A revision is carried out in several steps. First, a counterexample to this result is given, questioning its validity. Then an alternative statement is proposed, together with a detailed proof. Among the facts revealed is the relaxation of the assumption on a key parameter of the integral norm. Finally, several examples of the revised result are presented, showing a new modification of the Hardy integral inequality. Their originality takes advantage of the combined convexity and submultiplicativity assumptions, which remain an underexplored framework.
Source: DergiPark (Istanbul University)
Author: Chesneau, Christophe
Institution: Université de Caen Normandie
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416552268
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