Integral inequalities using signed measures corresponding to majorization

• DOI: 10.1007/s13398-023-01409-7
• Publication Date: 2023-03-02T21:11:43Z
• Authors: László Horváth
• Keywords: Majorization; Jensen's inequality

Abstract In this paper we derive majorization type integral inequalities using measure spaces with signed measures. We obtain necessary and sufficient conditions for the studied to be satisfied. To apply our results, first generalize Hardy–Littlewood–Pólya Fuchs inequalities. Then deal nonnegativity of some integrals nonnegative convex functions. As a consequence, known characterization Steffensen–Popoviciu measures on compact intervals is extended arbitrary intervals. Finally, give satisfaction Jensen inequality Lah–Ribarič All considered problems are also special classes prove main assertions approximation results functions developed.