广义黏性逼近方法及其应用

黏性逼近方法在非扩张映射不动点问题的研究中扮演着重要的角色。提出了一类广义黏性逼近方法，在一定条件下，证明了该算法的收敛性.作为应用，将所得的收敛性结果应用于求解约束凸优化问题与双层优化问题。     

超富足半群及其子类

借助半群的Malcev积和公理化条件,对超富足半群及其子类进行了刻画,给出了超富足半群及其子类的若干特征.     

Fixed Point Theorem of {a,b,c} Contraction and Nonexpansive Type Mappings in Weakly Cauchy Normed Spaces

Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectively by {a,b,c}-ntype and {a,b,c}-ctype. We proved the following： 1. If T is {a,b,c}-ntype mapping, then inf{ ｜｜ T（x）-x｜｜ ：x C C} =0, accordingly T has a unique fixed point. Moreover, any sequence {Xn}n∈NN in C with limn→∞｜｜T（xn） - Xn｜｜ = 0 has a subsequence strongly convergent to the unique fixed point of T. 2. If T is {a,b,c}-ctype mapping, then T has a unique fixed point. Moreover, for any x∈C the sequence of iterates {Tn （x）}n∈N has subsequence strongly convergent to the unique fixed point of T. This paper extends and generalizes some of the results given in [2,4, 7] and [13].     

APPROXIMATING COMMON FIXED POINTS OF NEARLY ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings.We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.     

Fixed-Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.     

Asymptotically Nonexpansive Mappings in Modular Function Spaces

In this paper, we prove that if ρ is a convex, σ-finite modular function satisfying a Δ₂-type condition, C a convex, ρ-bounded, ρ-a.e. compact subset of L_ρ, and T: C → C a ρ-asymptotically nonexpansive mapping, then T has a fixed point. In particular, any asymptotically nonexpansive self-map defined on a convex subset of L¹(Ω, μ) which is compact for the topology of local convergence in measure has a fixed point.     

On Short Time Asymptotic Behavior of Some Symmetric Diffusions on General State Spaces

For conservative symmetric diffusions on a general state space (X,m), the short time asymptotic behavior of tlog _X 1 _A T _t 1 _B dm is investigated, where T _t is the associated semigroup and A and B are measurable subsets of X. It is proved that the superior limit is dominated by the inferior limit up to some absolute constant. When ₂ of the associated Dirichlet form is lower bounded, it is shown that the limit exists for any A and B, and is described by the intrinsic metric between them. Applications to infinite-dimensional spaces and fractals are given.     

Fuzzy Ordered Filters in Negatively Partially Ordered Semigroups

本文将引入负偏序半群的Ｆｕｚｚｙ序滤子的概念，并研究Ｆｕｚｚｙ序滤子成为序滤子的充要条件及Ｆｕｚｚｙ序滤子的结构性质     

The null controllability of thermoelastic plates and singularity of the associated minimal energy function

We consider the null controllability problem for thermoelastic plates, defined on a two dimensional domain Ω, and subject to hinged, clamped or free boundary conditions. The uncontrolled partial differential equation system generates an analytic semigroup on the space of finite energy. Consequently, the concept of null controllability is indeed appropriate for consideration here. It is shown that all finite energy states can be driven to zero by means of just one L2((0,T)×Ω) control be it either mechanical or thermal. The singularity, as T↓0, of the associated minimal energy function is the main object studied in the paper. Singularity and blow-up rates for minimal energy function are not only of interest in their own right but are also of critical importance in Stochastic PDEs. In this paper, we establish the optimal blow-up rate for this function. It is shown that the rate of singularity is the same as for finite-dimensional truncations of the model. In view of sharp estimates available in the finite dimensional setting [Math. Control Signals Systems 9 (1997) 327], the singularity rates provided in this paper are optimal.