Some Opial type inequalities in (p, q)-calculus

In this paper, we establish 5 kinds of integral Opial-type inequalities in (p, q)-calculus by means of Hölder’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)...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 6; pp. 5893 - 5902
Main Authors Li, Chunhong, Yang, Dandan, Bai, Chuanzhi
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
opial inequality
opial-type integral inequality
q )-calculus
q )-integral
q)-derivative
Online AccessGet full text

Cover

More Information
Summary:In this paper, we establish 5 kinds of integral Opial-type inequalities in (p, q)-calculus by means of Hölder’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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020377