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Abstract and Applied Analysis
Volume 2017 (2017), Article ID 5234181, 7 pages
https://doi.org/10.1155/2017/5234181
Research Article

On Weighted Montgomery Identity for Points and Its Associates on Time Scales

Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, USA

Correspondence should be addressed to Eze R. Nwaeze; ude.eegeksut.utym@ezeawne

Received 21 March 2017; Accepted 6 June 2017; Published 30 July 2017

Academic Editor: Patricia J. Y. Wong

Copyright © 2017 Eze R. Nwaeze and Ana M. Tameru. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is to establish a weighted Montgomery identity for points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for points. For we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.