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

被引：7

作者：

Li, Chunhong ^{[1
]}

Yang, Dandan ^{[2
]}

Bai, Chuanzhi ^{[2
]}

机构：

[1] Journal Huaiyin Normal Univ, Editorial Dept, Huaian 223300, Jiangsu, Peoples R China

[2] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China

来源：

AIMS MATHEMATICS | 2020年 / 5卷 / 06期

关键词：

(p; q)-derivative; q)-integral; q)-calculus; Opial inequality; Opial-type integral inequality;

D O I：

10.3934/math.2020377

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

I n this paper, we establish 5 kinds of integral Opial-type inequalities in (p, q)-calculus by means of Holder'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.

引用

页码：5893 / 5902

页数：10

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