Some improvements of McShane and Hölder-type inequalities via superquadratic functions

In this paper, we obtain some new improvements of McShane’s and Hölder’s inequalities for positive linear functionals. Then, we apply our results to time-scale integrals and obtain new inequalities for time-scale integrals.

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Bibliographic Details
Published in:Journal of inequalities and applications 2024-11, Vol.2024 (1), p.146-13, Article 146
Main Authors: Rani, Shumaila, Bibi, Rabia
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Applied mathematics
Euclidean space
Functionals
Hölder’s inequality
Inequalities
Integrals
Mathematical functions
Mathematics
Mathematics and Statistics
McShane’s inequality
Positive linear functionals
Superquadratic functions
Time-scale calculus
Variables
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Description
Summary:In this paper, we obtain some new improvements of McShane’s and Hölder’s inequalities for positive linear functionals. Then, we apply our results to time-scale integrals and obtain new inequalities for time-scale integrals.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03221-2