Quasiconformal Mappings and Weakly John Domains

Let D be a bounded domain in R~2 and c(≥1)be a constant.We say that D is a c-Johndomain if there exists x_0∈D such that for any x∈D,there must be a rectifiable curve γDwhich joins x and x_0,satisfying l(γ(x,y))≤cd(y,D)for any y ∈γ,where l(γ(x,y))denotesthe Euclidean length of the subcurce γ between x and y,d(y,D)is the Euclidean distance fromy to the boundary D of D.We say that D is a John domain if D is a c-John domain for some     

Some Results Related to Metric Projection in Orlicz Sequence Spaces

Let X be a Banach space,and D a subset of X.A metric projection PD:X→ 2 Dis de-fined by PD(x) ={ y∈ D:‖ x-y‖ =d(x,D) } .D is a proximal (resp.Chebysev) setif PD contains at least(resp.exactly) one point.For a proximal set D,PD is callednorm-norm(norm-week) upper semi-continuous at x if for every normed(weak) openset W PD,there exists a normed neighborhood U of x such that PD(y) W for all y inU.It is proved in[1 ] that if X has C- (C- ) property PDis continuous for a Cheby-sev…     

Generalized Derivations with Nilpotent Values on Semiprime Rings

Let R be a semiprime ring, RF be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of RE. Furthermore, if there exists a fixed positive integer n such that μ(x)^n = 0 for all x∈I, then μ=0.     

On Universally Left-stability of ε-Isometry

LetX,Y be two real Banach spaces andε≥0.A map f:X→Y is said to be a standardε-isometry if|f(x)f(y)x y|≤εfor all x,y∈X and with f(0)=0.We say that a pair of Banach spaces(X,Y)is stable if there existsγ0 such that,for every suchεand every standardε-isometry f:X→Y,there is a bounded linear operator T:L(f)≡spanf(X)→X so that T f(x)x≤γεfor all x∈X.X(Y)is said to be universally left-stable if(X,Y)is always stable for every Y(X).In this paper,we show that if a dual Banach space X is universally left-stable,then it is isometric to a complemented w-closed subspace of∞(Γ)for some setΓ,hence,an injective space;and that a Banach space is universally left-stable if and only if it is a cardinality injective space;and universally left-stability spaces are invariant.     

Maximal Quotient Rings of Endomorphisms of Quasigenerators

O.Preliminaries. Let R be an associative ring with identity, and let Mod-R denote the category of all unital right R-modules. A set of right ideal of R is called a Gabriel topology on R if satisfies T1. If I∈ and I J, then J∈. T2. If I and J belong to, then I∩J∈. T3. I∈ and r∈R, then (I:r)={x∈R:rx∈I}∈. T4. If I is a right ideal of R and there exists J∈ such that (I:r)∈ for every r∈J, then I∈.     

Weighted Norm Inequalities for Multipliers and Littlewood-Paley Functions on Local Fields

Let K be a local field, w(x) be a A_p-weight on K (1≤p≤∞). We say that the measurable function m(x) is a multiplier on L~p(K,w), if (m)~v ∈L~p(K,w) for all f∈L~p(K,w) and there is a constant c>0,independent of f such that ‖(m     

ON THE EQUIVALENCE PRINCIPLE FOR CONTRACTIVE MAPPINGS

The main result is:Theorem 1.Let T be a continuous selfmapping of a complete metric space(X,d)andhave the unique fixed point property.If there exists n:X→N(the set of all positive integers)which is locally bounded such that for each x∈X and for all r∈N,r≥n(x),D(O_T(T~(n(x))x,0,r))≤(?)(D(O_T(x,0,r))),orD(O_T(T~(n(x))x,0,r))≤(?)(D(O_T(x,0,r))),where(?),and(?)are contractive gauge functions,then(a)T has a unique fixed point x~*;(b)For each x∈X,T~nx→x~* as n→∞;(e)There exists a neighborhood U(x~*)of x~* such that(?)T~n(U(x~*))={x~*};(d)x~*is stable;(e)For any given C∈(0,1)there exists a metric d~* topologically equivalent to d suchthat T is a Banach contraction under d~* with Lipschitz constant C.By Theorem 1 it is shown that many contractive type mappings defined in[1—26]aretopologically equivalent to each other.     

THE （u＋К）-ORBIT OF ESSENTIALLY NORMAL OPERATORS AND COMPACT PERTURBATIONS OF STRONGLY IRREDUCIBLE OPERATORS

Let Н be a complex,separable,infinite dimensional Hilbert space,T∈L(Н),(U+κ)(T) denotes the (U+κ)-orbit of T,i.e.,(U+κ)(T)={R^-1 TR:R is invertible and of the form unitary plus compact}.Let Ω be an analytic and simply connected Cauchy domain in C and n∈N,A（Ω,n）denotes the class of operators,each of which satisfies (i) T is essentially normal;(ii)σ(T)=Ω^-,ρF（T）∩σ（T）=Ω;（iii）ind(λ-T)=-n,nul(λ-T)=0,(λ∈Ω）。it is proved that given T1,T2∈A(Ω,n）and c>0,there exists a compact operator K with ||K||<ε such that T1+K∈(u+κ)(T2),this result generalizes a result of P.S.Guinand and L.Marcoux[6,15],Furthermore,the authors give a character of the norm closure of (u+κ)(T),and prove that for each T∈А(Ω,n）,there exists a compact (SI) perturbation of T whose norm can be arbitrarily small.     

A note on the density of a subset of all integrable holomorphic quadratic differentials

Let T0(Δ) be the subset of the universal Teichm¨uller space, which consists all of the elements with boundary dilatation 1. Let SQ(Δ) be the unit ball of the space Q(Δ) of all integrable holomorphic quadratic differentials on the unit disk Δ and Q0(Δ) be defined as Q0(Δ) = {? ∈ SQ(Δ) : there exists a k ∈(0, 1) such that [kˉ? |?|] ∈ T0(Δ)}. In this paper, we show that Q0(Δ) is dense in SQ(Δ).     

Approximation of the Cubic Functional Equations in Lipschitz Spaces

Let G be an Abelian group and let ρ : G×G→[0,∞) be a metric on GLet E be a normed spaceWe prove that under some conditions if f : G→E is an odd function and Cx : G→E defined by Cx(y) := 2 f(x + y) +2 f(x-y) + 12 f(x)-f(2x + y)-f(2x-y)is a cubic function for all x∈G, then there exists a cubic function C : G→E such that f-C is LipschitzMoreover, we investigate the stability of cubic functional equation2 f(x + y) + 2 f(x-y) + 12 f(x)-f(2x + y)-f(2x-y) = 0 on Lipschitz spaces.     

一致凸Banach空间非扩张映象带误差的Ishikawa型的三重迭代序列的收敛性

在一致凸Banach空间上,研究了半紧的非扩张压缩映象‖Tx-Ty‖≤‖x-y‖的Ishikawa型的三重迭代序列的收敛性问题,建立并证明了带误差的Ishikawa三重迭代逼近收敛定理,从而独特的推广了Mann和Ishikawa迭代方法,改进和发展了文献[1]-[7]的主要结果.     

Lipschitz强增生算子方程逼近解的带误差的Ishikawa迭代程序

设E是任意实Banach空间，T：E→E是Ligpschitz的强增生算子。证明了带误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解。特别地，还给出了Ishikawa迭代序列的收敛率估计。另一方面，一个相关结果，讨论了E中Lipschitz强伪压缩映象的不动点的带误差的Ishikawa迭代序列的收敛性。     

一致凸Banach空间非扩张映象的修正Ishikawa迭代序列的强收敛

在一致凸Banach空间上，研究了半紧的非扩张压缩映象的修正Ishikawasa三重迭代序列的强收敛问题，建立并证明了若干强收敛定理，推广了Mann和Ishikawa的迭代方法，改进和发展了Xu和贾如鹏等作者的主要结果．     

关于增生算子方程解的带误差的Ishikawa迭代程序

该文在Banach空间中证明了，带误差的Ishikawa迭代序列强收敛到Lipschitz连续的增生算子方程的唯一解．而且，也给Ishikawa迭代序列提供了一般的收敛率估计．利用该结果还推得，带误差的Ishikawa迭代序列也强收敛到Lipschitz连续的强增生算子方程的唯一解．     

Banach空间中几乎渐近非扩张型映象的不动点的迭代逼近

在Banach空间中引入了一类新的几乎渐近非扩张型映象,概括了Banach空间中若干熟知的非线性的Lipschitz映象类与非Lipschitz映象类成特例;例如,熟知的非扩张映象类,渐近非扩张映象类与渐近非扩张型映象类.考虑了用于逼近几乎渐近非扩张型映象不动点的带误差的修改了的Ishikawa迭代序列的收敛性问题.关于Banach空间范数的S.S.Chang的不等式与H.K.Xu的不等式皆被用于做精确不动点与近似不动点间的误差估计.而且,张石生教授用于做带误差的修改了的Ishikawa迭代序列收敛性分析的方法(应用数学和力学,2001,22(1):23-31)被推广到几乎渐近非扩张型映象的情况.给出了用于求一致凸Banach空间中几乎渐近非扩张型映象不动点的带误差的修改了的Ishikawa迭代序列的新的收敛判据.并且,由该判据,立即得到了此类映象的带误差的修改了的Mann迭代序列的新的收敛判据.上述结果统一、改进与推广了张石生教授关于用带误差的修改了的Ishikawa与Mann迭代序列来逼近渐近非扩张型映象不动点方面的结果.     

Φ-伪压缩映象带混合型误差的迭代序列的强稳定性

引入带混合型误差的 Ishikawa和 Mann迭代序列 ,在没有 D是有界闭集与多值映象 T是一致连续的较弱条件下 ,在实 Banach空间中研究了多值Φ -伪压缩映象不动点的带混合型误差的 Ishikawa和 Mann迭代序列的逼近问题 ,使用与文献完全不同的方法 ,建立了带混合型误差的 Ishikawa和 Mann迭代序列的强稳定性定理 ,从而统一和发展了几位作者早期与最近的相关结果 .     

含k-次增生算子方程（1–k）x＋Tx=f解的Ishikawa迭代逼近

在一致光滑的实Banach空间中,研究当T为k-次增生算子时,非线性方程（1-k）x＋Tx=f具混合误差的Ishikawa迭代解,给出了强收敛定理,并对Ishikawa迭代程序关于含k-次增生算子方程（1-k）x＋Tx=f的稳定性进行了讨论,推广和改进了近期一些文献的相关结果.     

带误差的非扩张映象及强伪压缩映象的Ishikawa迭代序列的收敛性

主要研究了带误差的非扩张映象及强伪压缩映象的Ishikawa迭代序列的收敛性问题，推广了已知的相关结果。     

A necessary and sufficient condition for the strong convergence of Lipschitzian pseudocontractive mapping in Banach spaces

The purpose of this paper is to establish some necessary and sufficient conditions for the strong convergence of the Ishikawa iterative sequence and the Mann iterative sequence to a fixed point of pseudocontractive mapping in Banach spaces. Our results, to some extent, improve and extend the well-known result of [S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44(1) (1974) 147–150.] to Banach spaces.     

Banach空间中严格渐近伪压缩映象的收敛性问题

在一致凸的Banach空间中，采用新的证明方法研究了严格渐近伪压缩映象和渐近非膨胀映象带误差的修正的Mann和Ishikawa迭代程序的收敛性问题，不要求定义域、值域有界，且迭代系数更简单．