# Novel Diamond Alpha Bennett–Leindler Type Dynamic Inequalities and Their Applications

Novel Diamond Alpha Bennett–Leindler Type Dynamic Inequalities and Their Applications For the exponent ζ>1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\zeta >1$$\end{document}, the diamond alpha Bennett–Leindler type inequalities are established by developing two methods, one of which is based on the convex linear combinations of the related delta and nabla inequalities, while the other one is new and is implemented by using time scale calculus rather than algebra. These inequalities can be considered as the complementary to the classical ones obtained for 0<ζ<1.\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0<\zeta <1.$$\end{document} Since both methods provide different diamond alpha Bennett–Leindler type inequalities, we can obtain various diamond alpha unifications of the known delta and nabla Bennett–Leindler type inequalities. Moreover, the second method offers new Bennett–Leindler type inequalities even for the special cases such as delta and nabla ones. Moreover, an application of dynamic Bennett–Leindler type inequalities to the oscillation theory of the second-order half linear dynamic equation is developed and presented for the first time ever. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Malaysian Mathematical Sciences Society Springer Journals

# Novel Diamond Alpha Bennett–Leindler Type Dynamic Inequalities and Their Applications

, Volume 45 (3) – May 1, 2022
28 pages

/lp/springer-journals/novel-diamond-alpha-bennett-leindler-type-dynamic-inequalities-and-KWA54Zv3Ps
Publisher
Springer Journals
Copyright © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021
ISSN
0126-6705
eISSN
2180-4206
DOI
10.1007/s40840-021-01224-6
Publisher site
See Article on Publisher Site

### Abstract

For the exponent ζ>1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\zeta >1$$\end{document}, the diamond alpha Bennett–Leindler type inequalities are established by developing two methods, one of which is based on the convex linear combinations of the related delta and nabla inequalities, while the other one is new and is implemented by using time scale calculus rather than algebra. These inequalities can be considered as the complementary to the classical ones obtained for 0<ζ<1.\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0<\zeta <1.$$\end{document} Since both methods provide different diamond alpha Bennett–Leindler type inequalities, we can obtain various diamond alpha unifications of the known delta and nabla Bennett–Leindler type inequalities. Moreover, the second method offers new Bennett–Leindler type inequalities even for the special cases such as delta and nabla ones. Moreover, an application of dynamic Bennett–Leindler type inequalities to the oscillation theory of the second-order half linear dynamic equation is developed and presented for the first time ever.

### Journal

Bulletin of the Malaysian Mathematical Sciences SocietySpringer Journals

Published: May 1, 2022

Keywords: Diamond alpha calculus; Bennett’s inequality; Leindler’s inequality; Oscillation of the second-order half linear dynamic equation; 34N05; 26D10; 26E70

### References

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