Generalized weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales via a parameter function

Abstract

We prove generalized weighted Ostrowski and Ostrowski--Grüss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the continuous, discrete, and quantum cases, to obtain some interesting new inequalities.

This is a preprint of a paper whose final and definite form is with 'Journal of Mathematical Inequalities' (JMI), ISSN: 1846-579X (print), 1848-9575 (online), available at [http://jmi.ele-math.com]. Paper Submitted 23-Dec-2016; Revised 21-June-2017; Accepted 27-June-2017