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].     

90年代的广义度量空间理论

广义度量空间理论是一般拓扑学研究的重要课题。本文综述了90年代广义度量空间理论的成就，分析了它的主要研究课题，所取得的重要结果是国内学者在该方向的贡献。     

非奇H矩阵的充分条件

文章通过引进一类具有非零元素链的矩阵,利用α对角占优矩阵性质,给出了一个新的非奇H矩阵的充分条件,扩大了非奇H矩阵的判定范围．     

关于非线性椭圆边值问题解的存在性的注

利用非线性增生映射值域的扰动理论,本文研究了与P拉普拉斯算子△p相关的非线性椭圆边值问题@在Ls(Ω)空间中解的存在性,其中2>sp>2nn+1且n1.@-Δpu+|u(x)|p-2u(x)+g(x,u(x))=fa.e.x∈Ω-〈υ,|u|p-2u〉=0a.e.x∈Γ其中f∈Ls(Ω)给定,ΩRn,n1,Δpu=div(|u|p-2u)为P拉普拉斯算子,υ为Γ的外法向导数,g∶Ω×R→R满足Caratheodory条件.本文所讨论的方程及所用的方法是对以往一些工作的补充和延续.     

L-Fuzzy代数的L-Fuzzy代数同态(英文)

本文研究了L-fuzzy代数的L-fuzzy代数同态的定义及其性质.利用L-fuzzy集的水平截集,得到TL-fuzzy代数的L-fuzzy代数同态的若干等价刻画.     

Stochastic flows of mappings

In this paper,the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied.This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.     

严格渐进伪压缩映象之修正型Mann迭代算法的强收敛性

本文利用CQ方法获得了k-严格渐进伪压缩映象修正型迭代算法的强收敛结果.此结果推广并改进了T.H.Kim和徐洪坤2006年获得的相应的一主要结果.即,从渐进非扩张映象推广到k-严格渐进伪压缩映象,并且去掉了闭凸子集C的有界性假设条件.     

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.     

Removable sets for continuous solutions of quasilinear elliptic equations

We show that sets of Hausdorff measure zero are removable for -Hölder continuous solutions to quasilinear elliptic equations similar to the -Laplacian. The result is optimal. We also treat larger sets in terms of a growth condition. In particular, our results apply to quasiregular mappings.