Diamond-<inline-formula> <graphic file="1029-242X-2008-576876-i1.gif"/></inline-formula> Jensen's Inequality on Time Scales
<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&qu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2008-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2008/576876 |
| Summary: | <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 Hölder's and Minkowski's diamond-<inline-formula> <graphic file="1029-242X-2008-576876-i4.gif"/></inline-formula> integral inequalities.</p> |
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| ISSN: | 1025-5834 1029-242X |