The Diamond Integral on Time Scales
Classical Analysis and ODEs
2015-09-11 v1
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.
Cite
@article{arxiv.1306.0988,
title = {The Diamond Integral on Time Scales},
author = {Artur M. C. Brito da Cruz and Natalia Martins and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1306.0988},
year = {2015}
}
Comments
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