A new variant of weighted Hermite-Hadamard inequalities and applications

• DOI: 10.48550/arxiv.2405.11701
• Publication Date: 2024-01-01
• Authors: Raissouli, Mustapha; Tarik, Lahcen; Chergui, Mohamed
• Keywords: Mathematics - Functional Analysis; Mathematics - Operator Algebras; FOS: Mathematics; Operator Algebras (math.OA); 47A63, 47A60, 47A64; Functional Analysis (math.FA)

In this article, we focus on establishing a new variant of Hermite-Hadamard type inequalities for operator convex maps using an appropriate probability measure. To underline the usefulness of these inequalities, we investigate some refinements of some well-known operator inequalities, as well as the definition of new weighted operator means.<br/>14 pages<br/>