共查询到20条相似文献,搜索用时 140 毫秒
1.
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
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S. M. Malamud 《Proceedings of the American Mathematical Society》2001,129(9):2671-2678
Motivated by an integral inequality conjectured by W. Walter, we prove some general integral inequalities on finite intervals of the real line. In addition to supplying new proofs of Walter's conjecture, the general inequalities furnish a reverse Jensen inequality under appropriate conditions and provide generalizations of Chebyshev's integral inequality. 相似文献
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Qiong Liu 《Mathematical Methods in the Applied Sciences》2021,44(1):593-604
By using some real analysis techniques, we study the structural characteristics of a multi‐parameter Hilbert‐type integral inequality with the hybrid kernel and obtain some equivalent conditions for this inequality. We also consider the operator expression of the equivalent inequalities. The conclusions not only integrate some results of references but also find some new Hilbert‐type integral inequalities with simple form by choosing suitable parameter values. 相似文献
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研究了带积分核函数和参数λ(λ〉1)的Hardy-Hilbert型不等式,并利用加强的Hlder’s不等式对Hardy-Hilbert不等式作了改进,建立了一些新的不等式. 相似文献
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《Journal of Functional Analysis》2023,284(4):109783
We prove some Lorentz-type estimates for the average in time of suitable geodesic interpolations of probability measures, obtaining as a by product a new estimate for transport densities and a new integral inequality involving Wasserstein distances and norms of gradients. This last inequality was conjectured in a paper by S. Steinerberger. 相似文献
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B.G Pachpatte 《Journal of Mathematical Analysis and Applications》1980,76(1):58-71
The aim of this paper is to establish some new partial integral inequalities in two independent variables which can be used in the analysis of a class of nonlinear non-self-adjoint hyperbolic partial integrodifferential equations. An elementary method of reducing the integral inequality to a second-order partial differential inequality and then integrating it by Riemann's method is used to establish our results. 相似文献
10.
Muhammad Adil Khan Shahid Khan Samet Erden Muhammad Samraiz 《Mathematical Methods in the Applied Sciences》2022,45(1):36-48
There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory. 相似文献
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证明了半序线性空间上线性泛函的两个Gr\"{u}ss型不等式, 并由此给出了Karamata型积分不等式的一种推广形式,
得到了一个新的Gr\"{u}ss型积分不等式及关于傅立叶系数的两个不等式.
最后利用所得结论研究了关于矩阵及线性算子的一些Gr\"{u}ss型不等式. 相似文献
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Zhao Ping Meng Fanwei 《Annals of Differential Equations》2006,22(1):113-118
We prove some new retarded nonlinear integral inequality and present its applications to the global existence of differential equations with delay. 相似文献
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This paper discusses some Cauchy-Khinchin integral inequalities. Khinchin [2] obtained an inequality relating the row and column sums of 0-1 matrices in the course of his work on number theory. As pointed out by van Dam [6], Khinchin’s inequality can be viewed as a generalization of the classical Cauchy inequality. Van Dam went on to derive analogs of Khinchin’s inequality for arbitrary matrices. We carry this work forward, first by proving even more than general matrix results, and then by formulating them in a way that allows us to apply limiting arguments to create new integral inequalities for functions of two variables. These integral inequalities can be interpreted as giving information about conditional expectations. 相似文献
14.
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
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以Hilbert不等式为代表的双线型不等式是分析学的重要不等式.应用权函数方法,引入多个参数,建立了一个新的具有最佳常数因子的-4齐次核的双线型不等式.作为应用,导出其等价形式及一些特殊结果. 相似文献
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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
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B. G. Pachpatte 《Periodica Mathematica Hungarica》1986,17(2):119-125
The aim of the present paper is to establish some new integral inequalities involving three functions and their derivatives which in the special cases yield the well known Opial inequality and some of its generalizations. 相似文献
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Some new nonlinear integral inequalities that involve the maximum of the unknown scalar function of one variable are solved. The inequalities considered are generalizations of a classical nonlinear integral inequality of Bihari. The importance of these integral inequalities is defined by their wide applications in qualitative investigations of differential equations with “maxima”, which is illustrated by some direct applications. 相似文献
20.
We establish various inequalities for n-times differentiable
mappings that are connected with illustrious Hermite-Hadamard
integral inequality for mapping whose absolute values of
derivatives are $\left( {\alpha ,m} \right)$-preinvex function.
The new integral inequalities are then applied to some special
means 相似文献