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)...

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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
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Abstract 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.
AbstractList 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.
Author Yang, Dandan
Bai, Chuanzhi
Li, Chunhong
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CorporateAuthor 1 Editorial Department of Journal of Huaiyin Normal University, Huai an, Jiangsu Province, 223300, China
2 School of Mathematical Science, Huaiyin Normal University, Huai an, Jiangsu Province, 223300, China
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SubjectTerms opial inequality
opial-type integral inequality
q )-calculus
q )-integral
q)-derivative
Title Some Opial type inequalities in (p, q)-calculus
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