A measure-theoretic version of the Dragomir-Jensen inequality
Abstract: We extend Dragomir's refinement of Jensen's inequality from the discrete to the general case, identifying the equality conditions.
- [Al] Aldaz, J. M. Comparison of differences between arithmetic and geometric means. Tamkang J. of Math., to appear. Available at the mathematics arXiv.
- [Dra] Sever S. Dragomir, Bounds for the normalised Jensen functional, Bull. Austral. Math. Soc. 74 (2006), no. 3, 471–478. MR 2273755, 10.1017/S000497270004051X
J. M. Aldaz
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
Keywords: Self-improvement, Jensen’s inequality
Received by editor(s): December 31, 2010
Received by editor(s) in revised form: February 16, 2011, and February 18, 2011
Published electronically: November 7, 2011
Additional Notes: This work was partially supported by Grant MTM2009-12740-C03-03 of the D.G.I. of Spain
Communicated by: Edward C. Waymire
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.