The Diamond Integral on Time Scales

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

References in corpus (3)

• Diamond-$\alpha$ Jensen's Inequality on Time Scales
• Symmetric Differentiation on Time Scales
• Hahn's Symmetric Quantum Variational Calculus

Cited by in corpus (2)

• Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets
• The fuzzy Henstock-Kurzweil delta integral on time scales