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

被引：5
|
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
收藏
页码：5893 / 5902
页数：10
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