Diamond-<inline-formula> <graphic file="1029-242X-2008-576876-i1.gif"/></inline-formula> Jensen's Inequality on Time Scales

• Main Authors: Sidi Ammi MoulayRchid, Ferreira RuiAC, Torres DelfimFM
• Format: Article
• Language: English
• Published: SpringerOpen 2008-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2008/576876

<p>Abstract</p> <p>The theory and applications of dynamic derivatives on time scales have recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-<inline-formula> <graphic file="1029-242X-2008-576876-i2.gif"/></inline-formula> derivatives which are a linear combination of delta and nabla dynamic derivatives on time scales. We prove a generalized version of Jensen's inequality on time scales via the diamond-<inline-formula> <graphic file="1029-242X-2008-576876-i3.gif"/></inline-formula> integral and present some corollaries, including H&#246;lder's and Minkowski's diamond-<inline-formula> <graphic file="1029-242X-2008-576876-i4.gif"/></inline-formula> integral inequalities.</p>