Inequality for 3-convex and 4-convex functions
Abstract
Abstract The inequality for 3-convex functions is established, which is a generalization of Levinson inequality and can unify some Ky Fan type inequalities, power mean inequality can also be refined. The inequality for 4-convex functions is also established, Ky Fan type inequality is refined on a deeper layer and some other special cases are also mentioned. As the obvious advantage of these basic inequalities for higher-order-convex function, Jensen inequality for convex function can be deduced from both inequality for 3-convex function and inequality for 4-convex function. Our proof is based on a lemma for convex function and detailed analysis for integral of derivative function.
Fields of Study & Subjects
Mathematical Inequalities and Applications
Functional Equations Stability Results
Analytic and geometric function theory
Publication details
- Journal / source
- Mathematica Slovaca
- Publisher
- Walter de Gruyter GmbH
- Volume
- 76
- Issue
- 1
- Pages
- 125–142
- Publication date
- 27 January 2026
- Language
- EN