鞅的矩型极大算子的若干不等式

给出了算子T=∑_(n=1)~∞T_n在H_B~p和BMO_(p,B)~-上有界的一些充分条件,其中T_n(n∈P)为具有Δ性质的算子.作为应用,借助于算子值鞅变换得到了关于鞅的矩型极大算子的强(p,p)型不等式和弱(1,1)型不等式,以及其在BMO_(p,B)~-上的有界性.这些结果与经典H~p鞅论中极大算子的性质相对应.     

Regularized collocation method for Fredholm integral equations of the first kind

In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number of collocation points plays the role of a regularization parameter. If the a priori information mentioned above is not available, then a combination of collocation with Tikhonov regularization can be the method of choice. We analyze such regularized collocation in a rather general setting, when a solution smoothness is given as a source condition with an operator monotone index function. This setting covers all types of smoothness studied so far in the theory of Tikhonov regularization. One more issue discussed in this paper is an a posteriori choice of the regularization parameter, which allows us to reach an optimal order of accuracy for deterministic noise model without any knowledge of solution smoothness.     

Banach空间中极大单调算子零点的迭代收敛定理及应用

令E为实光滑、一致凸的Banach空间,E*为其对偶空间.令A E×E*为极大单调算子且A-10≠.假设{rn}(0,+∞)为实数列且满足rn→∞,n→∞,数列{αn}[0,1]满足∑∞n=1(1-αn)<+∞,对给定的向量xn∈E,寻找向量{x∧n}及{en}使之满足:αnJxn+(1-αn)Jen∈Jx∧n+rnAx∧n,其中{en}E为误差序列而且满足一定的限制条件.即而定义迭代序列{xn}n 1如下:xn+1=J-1[βnJx1+(1-βn)Jx∧n],n 1,其中数列{βn}[0,1]满足βn→0,n→∞且∑∞n=1βn=+∞,则{xn}强收敛于QA-10(x1),这里QA-10为从E到A-10上的广义投影算子.利用Lyapunov泛函,Qr算子与广义投影算子等新技巧,证明了引入的新迭代序列强收敛于极大单调算子A的零点,并讨论了此结论在求解一类凸泛函最小值上的应用.     

含有各阶导数的高阶微分方程边值问题三个单调正解的存在性

利用五个泛函的不动点定理,研究一类含有各阶导数的2m阶微分方程边值问题的三个单调正解的存在性.     

Estimates for the Eigenvalues of Matrices

For matrices whose eigenvalues are real (such as Hermitian or real symmetric matrices), we derive simple explicit estimates for the maximal (λ_max) and the minimal (λ_min) eigenvalues in terms of determinants of order less than 3. For 3 × 3 matrices, we derive sharper estimates, which use det A but do not require to solve cubic equations.     

Equivalent quasi-norms on Lorentz spaces

We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.

     

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.      

Existence Theorems for Set-valued Operators in Banach Spaces

In this paper, we study the problem of existence of zero points for set-valued operators in Banach spaces. We present a simple condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive the surjectivity result and the Kakutani fixed point theorem by using this condition.      

混合单调算子的两点拉伸型不动点定理

本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究.