On an Extension and a Refinement of Van der Corput＇s Inequality

By introducing a parameterα,we give an extension of Van der Corput's inequal- ity.Also a new strengthened version of it is considered.     

多元Newman不等式与逼近逆定理

本文研究多元有理逼近的Newman不等式与逼近逆定理问题.在多元Müntz多项式空间中利用分解方法建立多元有理多项式的Markov型不等式与Nikolskii型不等式.同时,建立多元有理逼近的逆定理,即Steckin型不等式.本文所获结果不仅推广了一元的相应结果,而且包含了关于代数多项式的一些经典结果.     

Talagrand＇s T2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

Abstract We establish Talagrand’s T₂-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type’s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction-Diffusion equations are provided. * Project supported by the Yangtze Scholarship Program.     

Retraction Notice to ＂A Mathematical Proof a Probabilistic Model of Hardy＇s Inequality＂

The Editor-in-Chief, after being alerted that this article is essentially the same as [On an Argument of K6rner and Hardy＇s Inequality, M. Sababheh, Analysis Mathematica, 34（2008）, 51-57], requested the retraction of the paper.     

Extensions of Vietoris＇s Inequalities （I）

In 1958, L. Vietoris[10] proved that if α0 ≥ αl ≥ ... ≥ αn ≥ 0 and α2k ≤ (1-1/2k)α2k-1, k ≥ 1,then for n ≥ 1 and θ ∈ (O, π),     

Extensions and Refinements ofAdamovic＇s Inequality

In this article, by means of tile theory of majorization, Adamovic‘s inequality isextended to the cases of the general elementary symmetric functions and its duals, and therefined and reversed forms are also given. As applications, some new inequalities for simplexare established.     

Jensen’s Inequality for Backward Stochastic Differential Equations

Abstract Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen’s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g(t, 0) ≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen’s inequality for g- expectation in [4, 7–9]. *Project supported by the National Natural Science Foundation of China (No.10325101) and the Science Foundation of China University of Mining and Technology.     

On a Trigonometric Inequality of Vinogradov

In this paper, we improve an inequality of Vinogradov by analysis method.     

Kobayashi＇s and Teichmiiller＇s Metrics on the Teichmiiller Space of Symmetric Circle Homeomorphisms

We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi’s metric and Teichmüller’s metric coincide with each other on the Teichmüller space of symmetric circle homeomorphisms.     

Another Extension of the Mitrinovic—Djokovic Inequality

Another generalization of the Mitrinovic-Djokovic inequality is proved by elementarymeans.     

On a Generalization of Some Restrictive Distribution Theorems

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An Extension of the Mitrinovi‘c—Djokovi’c Inequality

A certain generalization of the Mitrinovi‘c-Djokovi‘c inequality is proved by means of elenen-tary calculus.     

Discrete Hardy-Hilbert＇s Inequalities in R^n

By using some auxiliary functions and introducing relative Lemmas, we establish multidimensional discrete Hardy-Hilbert‘s inequalities.     

Weierstrass不等式的新推广

利用控制不等式理论将 Weierstrass不等式 ∏ni=1( 1± xi) >1± ∑ni=1xi推广到一般初等对称函数上 ,并且给出一个上界估计 .     

Existence and Exponential Stability of Almost Periodic Solution for Hopfield Neural Network Equations with Almost Periodic Imput

By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. In this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.