共查询到20条相似文献,搜索用时 359 毫秒
1.
《Applied Mathematics Letters》2006,19(7):657-660
Using Hayashi’s inequality, an Iyengar type inequality for functions with bounded second derivative is obtained. This result improves a similar result from [N. Elezović, J. Pečarić, Steffensen’s inequality and estimates of error in trapezoidal rule, Appl. Math. Lett. 11 (6) (1998) 63–69] and, for some classes of functions, the result from [X.L. Cheng, The Iyengar type inequality, Appl. Math. Lett. 14 (2001) 975–978]. 相似文献
2.
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
3.
本文研究Hilbert积分不等式的推广问题.利用引入参数和对数积分核函数,建立了一种新的Hilbert型积分不等式,证明了用Euler数和π来表示的常数因子是最佳的,推广了经典的Hilbert积分不等式. 相似文献
4.
Detailed analysis shows that the famous Iyengar inequality actually says that the Trapezoidal formula is a central algorithm
for approximating integrals over an appropriate interval for the class of functions whose derivatives are bounded by a positive
number K in L
∞-sense. The inherent nonlinearity from central algorithms reflects the importance of the Iyengar inequality and thus makes
familiar linear methods malfunction when one tries to generalize it. It is shown that the generalization depends on a nonlinear
system of equations satisfied by a set of free nodes of a perfect spline. Explicit constructions are obtained in the spirit
of the Iyengar inequality for the class of functions whose rth (r≤4) derivatives are bounded by a positive number K in L
∞-sense because a closed solution to the nonlinear system is only available for r≤4. Connections with computational mathematics, especially with best interpolation and best quadrature, are discussed. Numerical
experiments are also included.
AMS subject classification (2000) 65D30, 41A17 相似文献
5.
杨恩浩 《应用数学学报(英文版)》2001,17(2):233-239
1. IntroductionIt is well known that integral inequalities are very crucial in the study of differelltialequations, integral equations, functional-differential equations, iniegro-differential equationsand evolution equations. Besides the famous Gronwall-Bellman inequality and its first nonlinear generalization due to i. Bihari (of. [1]), there is another very useful integral inequalityestablished by L. On-fang[2]:Lemma 1. Let u(t) and h(t) be real-valued, nonnegative and continuous functions… 相似文献
6.
刘建忠 《数学物理学报(A辑)》2012,32(1):171-185
利用H\"{o}lder不等式和β-函数, 得到了Hardy-Littlewood不等式的一些推广和改进形式. 作为应用, 通过所得结果及矩阵方法, 给出了Hilbert型不等式的一些推广和改进. 相似文献
7.
8.
This paper establishes a type of Kantorovich inequality subject to some constraints and obtains some lower bounds for the relative efficiency of the least squares. These lower bounds can be much sharper than that obtained by using the unconstrained Kantorovich inequality. Multivariate extensions of the results are also obtained. Some interesting examples are presented. 相似文献
9.
Shanhe Wu 《Journal of Mathematical Analysis and Applications》2005,308(2):689-702
In this paper, we establish two extensions of Weierstrass's inequality involving symmetric functions by means of the theory of majorization, and give an interesting sharpness of Weierstrass's inequality by using the arithmetic-geometric mean inequality. Furthermore, we apply these results to improve a well-known inequality and deduce some new inequalities. 相似文献
10.
一个不等式的简单证明与推广 总被引:1,自引:0,他引:1
本文讨论了一个引人注目而被广泛讨论的、与平均值有关的不等式.我们首先获得了它的完整形式,给出了一个非常简洁而能揭示问题本质的证明.由此我们自然地引出了它的最为一般的形式.同时,我们还指出文献中存在的一些谬误. 相似文献
11.
Riemann zeta function and Lyapunov-type inequalities for certain higher order differential equations
This note generalizes the well known Lyapunov-type inequalities for second-order linear differential equations to certain 2M-th order linear differential equations with five types of boundary conditions. The usage of the best constant of some Sobolev-type inequalities clarify the process for obtaining such inequality and sharpen the result of Çakmak [2]. 相似文献
12.
《Journal of Mathematical Analysis and Applications》1987,122(1):7-15
The purpose of this paper is to obtain some general inequalities which contain as special cases some recently established extensions of Hardy's integral inequality. 相似文献
13.
A. Osękowski 《Analysis Mathematica》2016,42(1):55-67
We present a new proof of Carlson–Levin inequality and some of its extensions, based on a dynamic programing-type approach. 相似文献
14.
P. Topping 《Commentarii Mathematici Helvetici》1997,72(2):316-328
We explore some geometric aspects of compensation compactness associated to Jacobian determinants. We provide the optimal
constant in Wente's inequality - the original motivation of this work - and go on to give various extensions to geometric
situations. In fact we improve Wente's inequality somewhat, making it more appropriate for applications in which optimal results
are required. This is demonstrated when we prove an optimal inequality for immersed surfaces of constant mean curvature in
, contolling their diameter in terms of their area and curvature.
Received: November 4, 1996 相似文献
15.
In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Maclaurin summation formula. We give the improvements of some previously obtained results and also compare our results with some previously known from the literature. 相似文献
16.
In this paper we shall generalize Shearer??s entropy inequality and its recent extensions by Madiman and Tetali, and shall apply projection inequalities to deduce extensions of some of the inequalities concerning sums of sets of integers proved recently by Gyarmati, Matolcsi and Ruzsa. We shall also discuss projection and entropy inequalities and their connections. 相似文献
17.
Ukrainian Mathematical Journal - For mappings with branching points satisfying the Poletsky inverse inequality, we obtain some results on their continuous boundary extensions in terms of prime... 相似文献
18.
S. Sadiq Basha 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):5844-5850
The primary objective of this article is to elicit some interesting extensions of the simple but powerful Banach’s contraction principle to the case of non-self-mappings. In fact, due to the fact that best proximity point theorems fit the bill to this end, the proposed extensions are presented as best proximity point theorems for non-self proximal contractions which are more general than the notion of self-contractions. 相似文献
19.
Anders Frankild 《代数通讯》2013,41(2):461-500
In this article we present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings. One primary focus is the descent of these properties over ring homomorphisms of finite flat dimension, presented in terms of inequalities between generalized G-dimensions. Most of these results are new even when the ring homomorphism is local. The main tool for these analyses is a nonlocal version of the amplitude inequality of Iversen, Foxby, and Iyengar. We provide numerous examples demonstrating the need for certain hypotheses and the strictness of many inequalities. 相似文献
20.
In the present paper we establish some new inequalities similar to extensions of Hilbert’s double-series inequality and give
also their integral analogues. Our results provide some new estimates to these types of inequalities. 相似文献