共查询到20条相似文献,搜索用时 17 毫秒
1.
Zareen A. Khan 《Integral Transforms and Special Functions》2020,31(5):412-423
ABSTRACTThis paper investigates some system of integral inequalities of one independent variable on time scales. The conclusion can be obtained by using Hadamard-type fractional differential equations and Greene's method which bring together and expand some integral inequalities on time scales. The established inequalities give explicit bounds on unknown functions which can be utilized as a key in examining the properties of certain classes of partial dynamic equations and difference equations on time scales. As an application, a system of fractional differential equations is considered to explain the value of our results. 相似文献
2.
该文利用单调化技巧研究了时标上的推广的Pachpatte型不等式, 该不等式右端有一个非常数项和三个包含未知函数与没有假设单调性的非线性函数的复合函数的积分项, 不等式左端是未知函数与非线性函数的复合函数. 所得不等式不仅把Pachpatte型不等式的离散形式和连续形式统一起来, 而且推广了已有的时标上的相应不等式. 最后, 用得到的结果研究时标上边值问题解的估计. 相似文献
3.
In the paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales. 相似文献
4.
Half-linear Volterra-Fredholm type integral inequalities on time scales and their applications
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Haidong Liu 《Journal of Applied Analysis & Computation》2020,10(1):234-248
The main aim of this paper is to establish some new half-linear Volterra-Fredholm type integral inequalities on time scales. Our results not only extend and complement some known integral inequalities but also provide an effective tool for the study of qualitative properties of solutions of some dynamic equations. 相似文献
5.
Some Generalized Gronwall-like Retarded Inequalities in two independent variables on Time Scales
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In this paper, we establish some new Gronwall-like inequalities in two independent variables which can be used as tools in the theory of integral equations with delay on time scales. 相似文献
6.
Mehmet Zeki Sarikaya 《Applied Mathematics Letters》2009,22(9):1340-1344
In this study, we establish some new weighted Iyengar type integral inequalities using Steffensen’s inequality on time scales. 相似文献
7.
In this paper, some Gronwall-Bellman type nonlinear delay integral inequalities on time scales are established, which provide a handy tool in deriving boundedness of solutions of certain delay dynamic equations on time scales. Our results generalize some of the main results in Lipovan (2006) [1], Pachpatte (2000) [2], Ferreira and Torres (2009) [3], Zhang and Meng (2008) [4], Cheung and Ren (2006) [5], Kim (2009) [6], and some of our results unify continuous and discrete analysis in the literature. 相似文献
8.
Wei Nian Li 《Journal of Mathematical Analysis and Applications》2006,319(2):802-814
In this paper, based on some known dynamic inequalities, we investigate certain new dynamic inequalities on time scales, which provide explicit bounds on unknown functions. Our results unify and extend some continuous inequalities and their corresponding discrete analogues. 相似文献
9.
《Mathematical Methods in the Applied Sciences》2018,41(12):4737-4753
In the present article, we investigate some new inequalities of Steffensen type on an arbitrary time scale using the diamond‐α dynamic integrals, which are defined as a linear combination of the delta and nabla integrals. The obtained inequalities extend some known dynamic inequalities on time scales and unify and extend some continuous inequalities and their discrete analogues. 相似文献
10.
In this paper, we prove some new dynamic inequalities on time scales using Hölder's inequality and Keller's chain rule on time scales. These inequalities, as special cases when the time scale and when , contain some generalizations of integral and discrete inequalities due to Hardy, Copson, Leindler and Bennett. 相似文献
11.
In this paper, we will prove some new dynamic Hardy-type inequalities on time scales with two different weighted functions. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. The main results will be proved by employing Hölder’s inequality, Minkowski’s inequality and a chain rule on time scales. As special cases of our results, when the time scale is the real numbers, we will derive some well-known results due to Copson, Bliss, Flett and Bennett by a suitable choice of the weighted functions. We will apply the results to investigate the oscillation and nonoscillation of a half-linear second order dynamic equation on time scales. 相似文献
12.
In this paper, we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski-type, Trapezoid-type, Grüss-type and Ostrowski–Grüss-like inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases. 相似文献
13.
The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds
on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities
related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl.
251 (2000) 736–751). 相似文献
14.
Murat Ad?var Elvan Ak?n Bohner 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7519-7531
This paper aims to introduce Halanay type inequalities on time scales. By means of these inequalities we derive new global stability conditions for nonlinear dynamic equations on time scales. Giving several examples we show that besides generalization and extension to q-difference case, our results also provide improvements for the existing theory regarding differential and difference inequalities, which are the most important particular cases of dynamic inequalities on time scales. 相似文献
15.
Sabir Hussain 《Aequationes Mathematicae》2013,85(3):409-419
Generalized Ostrowski and ?eby?ev type inequalities involving many functions on time scales are derived that generalize some existing and classical inequalities with some applications for generalized polynomials. 相似文献
16.
We establish some Iyengar-type inequalities on time scales for functions whose second derivatives are bounded by using Steffensen’s inequality on time scales. 相似文献
17.
In this paper, an N-species cooperation system with time delays and feedback controls is proposed on time scales. In this process, some inequalities, which play a vital roles in the proof of main results, are firstly proved. Then, by applying the theory of differential inequality, sufficient conditions which guarantee the permanence of the system are obtained on time scales. Our results improve and complement some known results to some degree in the literature. 相似文献
18.
The purpose of the present note is to establish some new delay integral inequalities, which provide explicit bounds on unknown functions and generalize some results of Li et al. [Some new delay integral inequalities and their applications, J. Comput. Appl. Math. 180 (2005) 191–200]. The inequalities given here can be used to investigate the qualitative properties of certain delay differential equations and delay integral equations. 相似文献
19.
In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of our's. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integro-differential equations with time delay. 相似文献
20.
一类积分不等式的推广 总被引:1,自引:0,他引:1
对一些基本的积分不等式进行了推广,给出了含有n个无关变元的更广泛的非线性积分不等式.利用所得的不等式讨论了某些非线性积分方程解的有界性. 相似文献