Weighted dynamic inequalities of Opial-type on time scales
TLDR
In this paper, the authors state and prove some weighted dynamic inequalities of Opial-type involving integrals of powers of a function and of its derivative on time scales which not only extend some results in the literature but also improve some of them.Abstract:
In this paper, we will state and prove some weighted dynamic inequalities of Opial-type involving integrals of powers of a function and of its derivative on time scales which not only extend some results in the literature but also improve some of them. The main results will be proved by using some algebraic inequalities, the Holder inequality and a simple consequence of Keller’s chain rule on time scales. As special cases of the obtained dynamic inequalities, we will get some continuous and discrete inequalities.read more
Citations
More filters
Journal ArticleDOI
On some new double dynamic inequalities associated with Leibniz integral rule on time scales
A. A. El-Deeb,Saima Rashid +1 more
TL;DR: In this paper, the authors give a new proof and formula of Leibniz integral rule on time scales and also apply their inequalities to discrete and continuous calculus to obtain some new inequalities as special cases.
Journal ArticleDOI
Dynamic Hilbert-Type Inequalities with Fenchel-Legendre Transform
TL;DR: This work generalizes a number of multiple inequalities illustrated in 2020 to a general time scale with the help of a Fenchel-Legendre transform and extends them to continuous and discrete calculus.
Journal ArticleDOI
Certain new dynamic nonlinear inequalities in two independent variables and applications
A. A. El-Deeb,Zareen A. Khan +1 more
TL;DR: In this article, Boudeliou, Abdeldain, El-Deeb and Pachpatte generalized these inequalities to time scales and applied them to discrete and continuous calculus.
Journal ArticleDOI
New Weighted Opial-Type Inequalities on Time Scales for Convex Functions
A. A. El-Deeb,Dumitru Baleanu +1 more
TL;DR: This work generalizes a number of multiple inequalities based on the multiple inequalities illustrated in 1967 to a general time scale with the help of the dynamic Jensen and Holder inequality.
Journal Article
Opial and Lypaunov type inequalities for half-linear dynamicequations
TL;DR: In this article, time scale versions of Opial's inequality and Lyapunov's inequality are presented, which unify, extend and generalize some of the existing results.
References
More filters
Book
Dynamic Equations on Time Scales: An Introduction with Applications
Martin Bohner,Allan Peterson +1 more
TL;DR: The Time Scales Calculus as discussed by the authors is a generalization of the time-scales calculus with linear systems and higher-order linear equations, and it can be expressed in terms of linear Symplectic Dynamic Systems.
BookDOI
Advances in dynamic equations on time scales
Martin Bohner,Allan Peterson +1 more
TL;DR: Agarwal et al. as discussed by the authors proposed a topological approach for solving two-point boundary value problems on infinite-intervals, using the time scales of the time-scales calculus.
Book
Uniqueness and nonuniqueness criteria for ordinary differential equations
TL;DR: First order differential equations first order differential systems higher order differential equation differential equations in abstract spaces complex differential equations functional differential equations impulsive differential equations differential equations with hysteresis generalized differential equations as mentioned in this paper.