On Hermite-Hadamard-type inequalities for second order differential inequalities with inverse-square potential

• Published in: AIMS mathematics Vol. 9; no. 7; pp. 17955 - 17970
• Main Authors: Aydi, Hassen, Samet, Bessem, De la Sen, Manuel
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: convex functions; convex functions on the coordinates; hermite-hadamard-type inequalities; second order differential inequalities

We consider the class of functions $ u\in C^2((0, \infty)) $ satisfying second-order differential inequalities in the form $ u''(x)+\frac{k}{x^2}u(x)\geq 0 $ for all $ x > 0 $. For this class of functions, we establish Hermite-Hadamard-type inequalities in both cases ($ k=\frac{1}{4} $...