Triple Diamond-Alpha integral and Hölder-type inequalities

In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and rev...

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Bibliographic Details
Published in:Journal of inequalities and applications 2018, Vol.2018 (1), p.1-14, Article 111
Main Author: Tian, Jing-Feng
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Diamonds
Hölder’s inequality
Inequalities
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Minkowski’s inequality
Time
Time scales
Triple Diamond-Alpha integral
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Summary:In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral. Moreover, using the obtained results, we give a new generalization of the Minkowski inequality for the triple Diamond-Alpha integral on time scales.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1704-0