Some Opial type inequalities in (p, q)-calculus
Open Access
- 1 January 2020
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 5 (6), 5893-5902
- https://doi.org/10.3934/math.2020377
Abstract
In this paper, we establish 5 kinds of integral Opial-type inequalities in (p, q)-calculus by means of H?lder's inequality, Cauchy inequality, an elementary inequality and some analysis technique. First, we investigated the Opial inequalities in (p, q)-calculus involving one function and its (p, q) derivative. Furthermore, Opial inequalities in (p, q)-calculus involving two functions and two functions with their (p, q) derivatives are given. Our results are (p, q)-generalizations of some known inequalities, such as Opial-type integral inequalities and (p, q)-Wirtinger inequality.Keywords
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