×

Refinements of Young’s integral inequality via fundamental inequalities and mean value theorems for derivatives. (English) Zbl 1455.26020

Dutta, Hemen (ed.), Topics in contemporary mathematical analysis and applications. Boca Raton, FL: CRC Press (ISBN 978-0-367-53266-6/hbk; 978-1-003-08119-7/ebook). Mathematics and its Applications: Modelling, Engineering, and Social Sciences, 193-228 (2021).
From the book’s preface: This chapter reviews several refinements of Young’s integral inequality via several mean value theorems, such as Lagrange’s and Taylor’s mean value theorems of Lagrange’s and Cauchy’s type remainders, and via several fundamental inequalities, such as Čebyšev’s integral inequality, Hermite-Hadamard’s type integral inequalities, Hölder’s integral inequality, and Jensen’s discrete and integral inequalities, in terms of higher-order derivatives and their norms. It also surveys several applications of several refinements of Young’s integral inequality and further refines Young’s integral inequality via Pólya’s type integral inequalities.
For the entire collection see [Zbl 1453.00001].

MSC:

26D15 Inequalities for sums, series and integrals
PDFBibTeX XMLCite
Full Text: DOI arXiv