Abstract
AbstractIn this paper we derive majorization type integral inequalities using measure spaces with signed measures. We obtain necessary and sufficient conditions for the studied integral inequalities to be satisfied. To apply our results, we first generalize Hardy–Littlewood–Pólya and Fuchs inequalities. Then we deal with the nonnegativity of some integrals with nonnegative convex functions. As a consequence, the known characterization of Steffensen–Popoviciu measures on compact intervals is extended to arbitrary intervals. Finally, we give necessary and sufficient conditions for the satisfaction of the integral Jensen inequality and the integral Lah–Ribarič inequality for signed measures. All the considered problems are also studied for special classes of convex functions. To prove the main assertions some approximation results for nonnegative convex functions are also developed.
Funder
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Reference17 articles.
1. Barnett, N.S., Cerone, P., Dragomir, S.S.: Majorisation inequalities for Stieltjes integrals. Appl. Math. Lett. 22, 416–421 (2009)
2. Chong, K.M.: Some extensions of a theorem of Hardy, Littlewood and Pólya and their applications. Can. J. Math. 26, 1321–1340 (1974)
3. Dahl, G.: Matrix majorization. Linear Algebra Appl. 288, 53–73 (1999)
4. Florea, A., Niculescu, C.P.: A Hermite-Hadamard inequality for convex–concave symmetric functions. Bull. Math. Soc. Sci. Math. Roumanie 50, 149–156 (2007)
5. Fuchs, L.: A new proof of an inequality of Hardy, Littlewood and Pólya. Mat. Tidsskr. B 1947, 53–54 (1947)
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