descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 17 Dec 2014Embargo end date: 01 Jan 2013 English Publisher:Springer Science and Business Media LLCJournal:Bulletin of the Malaysian Mathematical Sciences Society, volume 38, pages 1,453-1,462 (issn: 0126-6705, eissn: 2180-4206,

Authors: Brito da Cruz, A. M. C.; Martins, N.; Torres, D. F. M.;

doi: 10.1007/s40840-014-0096-7 , 10.48550/arxiv.1306.0988

arXiv: http://arxiv.org/abs/1306.0988

handle: 10773/14655

The Diamond Integral on Time Scales

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Abstract

We define a more general type of integral on time scales. The new diamond integral is a refined version of the diamond-alpha integral introduced in 2006 by Sheng et al. A mean value theorem for the diamond integral is proved, as well as versions of Holder's, Cauchy-Schwarz's and Minkowski's inequalities.

This is a preprint of a paper whose final and definite form will appear in the Bulletin of the Malaysian Mathematical Sciences Society. Paper submitted 12-Feb-2013; revised 07-May-2013; accepted for publication 05-Jun-2013

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Keywords

Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 26D15, 26E70, Diamond integral, Integral inequalities, Time scales

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