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Open AccessArticle

New Weighted Opial-Type Inequalities on Time Scales for Convex Functions

1
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt
2
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
3
Institute of Space Science, 07650 Magurele-Bucharest, Romania
4
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(5), 842; https://doi.org/10.3390/sym12050842
Received: 21 March 2020 / Revised: 21 April 2020 / Accepted: 1 May 2020 / Published: 21 May 2020
(This article belongs to the Special Issue Composite Structures with Symmetry)
Our work is based on the multiple inequalities illustrated in 1967 by E. K. Godunova and V. I. Levin, in 1990 by Hwang and Yang and in 1993 by B. G. Pachpatte. With the help of the dynamic Jensen and Hölder inequality, we generalize a number of those inequalities to a general time scale. In addition to these generalizations, some integral and discrete inequalities will be obtained as special cases of our results. View Full-Text
Keywords: opial-type inequality; dynamic inequality; convexity; time scale opial-type inequality; dynamic inequality; convexity; time scale
MDPI and ACS Style

El-Deeb, A.A.; Baleanu, D. New Weighted Opial-Type Inequalities on Time Scales for Convex Functions. Symmetry 2020, 12, 842.

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