一个构造增生映像零点的带误差的迭代算法

设E是一致光滑的Banach空间,A:D(A)E→2~E是一个满足值域条件的增生算子,进一步满足线性增长条件:‖Ax‖≤C(1+‖x‖)对某个常数C0, x∈D(A).设z∈D(A)是任意固定元,x_1∈D(A), A~(-1)0≠Φ.定义序列{x_n}D(A)如下:x_(n+1)∈x_n-λ_n(Ax_n+θ_n(x_n-z+e_n)),n≥1,其中{λ_n}与{θ_n}是满足一定条件的非负数列.则x_n→x~*∈A~(-1)(0),(n→∞).作为应用,我们推出构造连续伪压缩映像的不动点的收敛定理.     

非扩张映射和广义变分不等式的粘滞逼近法

应用已提出的非扩张映射的粘滞逼近方法,给定初值x_0∈C,考虑一般迭代过程{x_n},g(x_(n+1))=α_nf(x_n)+(1-α_n)SP_C(g(x_n)-λ_nAx_n),n≥0,其中{α_n}■(0,1),S:C→C是非扩张映射,C是实Hilbert空间H的非空闭凸子集.在{α_n}满足合适的条件下可证明,{x_n}强收敛到非扩张映射的不动点集和广义变分不等式解的公共元,且满足某变分不等式.     

广义Lipschitz伪压缩映射黏滞迭代逼近方法的强收敛

K是Banach空间E的一个非空闭凸子集,T:K→K是一个广义Lipschitz伪压缩映射.对Lipschitz强伪压缩映射f:K→K和x_1∈K,序列{x_n}由下式定义:x_n+1=(1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.在{α_n}与{β_n}满足合适条件的情况下,每当{z∈K;μ_n‖x_n-z‖~2=inf_(y∈K)μ_n‖x_n-y‖~2}∩F(T)≠φ时,{x_n}强收敛到T的某个不动点x~*.     

增生算子粘性逼近的强收敛定理

假设$E$为实Banach空间, $A$为具有零点的增生算子. 定义序列 $\{x_n\}$如下: $x_{n+1}=\alpha_n f(x_n)+(1-\alpha_n)J_{r_n}x_n$, 这里$\{\alpha_n\}$, $\{r_n\}$ 满足一定条件的序列, 令$J_r=(I+rA)^{-1}$, $r>1$. 假如空间$E$有弱连续对偶映像,或者$E$为一致光滑的,均得到了序列 $\{x_n\}$的强收敛性结果.     

非线性算子具误差的隐迭代程序的强收敛性

设K是一致凸Banach空间中的非空闭凸子集,T_i:K→K(i=1,2,…,N)是有限族完全渐近非扩张映象.对任意的x_0∈K,具误差的隐迭代序列{x_n}为:x_n=α_nx_n-1+β_nT_n~kx_n+γ_nu_n,n≥1,其中{α_n},{β_n},{γ_n}■[0,1]满足α_n+β_n+γ_n=1,{u_n}是K中的有界序列.在一定的条件下,该文建立了隐迭代序列{x_n}的强收敛性.得到隐迭代序列{x_n}强收敛于有限族完全渐近非扩张映象公共不动点的充要条件.所得结果改进和推广了Shahzad与Zegeye,Zhou与Chang,Chang,Tan,Lee与Chan等人的相应结果.     

迭代逼近m-增生映象的零点

设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的.设A是m-增生映象,使得C=■是E的凸子集,数列{α_n)■[0,1],{r_n}■ (0,∞),在适当的条件下,则由(1.2)式定义的迭代序列{x_n}强收敛于A~(-1)(0)中的点.其次证明了:设E是一致凸Banach空间,其范数是Frechet可微的.设数列{α_n},{β_n)■(0,1),{r_n}■(0,∞),满足适当的条件.如果A~(-1)(0)∩B~(-1)(0)≠φ,则由(3.20)式定义的序列{x_n}弱收敛于A~(-1)(0)∩B~(-1)(0)中的点.其结果推广和改进了Kamimura,Takahashi(2000)的定理2及Xu H.K.(2006)的定理4.1,定理4.2和定理4.3:(i)Kamimura,Takahashi(2000)定理2中的假设"自反Banach空间E的每个有界闭凸子集对非扩张自映象有不动点性质"被去掉;(ii)Xu H.K.(2006)的假设"E是具有弱连续对偶映象J_φ的自反Banach空间",被本文的假设"E是具有一致正规结构且其范数是一致Gateaux可微的Banach空间"所取代.从而补充了Xu H.K.(2006)未包含的另外一些Banach空间.同时还证明了逼近两个m-增生映象的公共零点,其结果也推广和改进了Mainge的相应结果.     

Banach空间非扩张映像不动点强收敛定理

设E是具弱序列连续对偶映像自反Banach空间, C是E中闭凸集, T:C→ C是具非空不动点集F(T)的非扩张映像.给定u∈ C,对任意初值x0∈ C,实数列{αn}n∞=0,{βn}∞n=0∈ (0,1),满足如下条件:(i)sum from n=α to ∞α_n=∞, α_n→0;(ii)β_n∈[0,α) for some α∈(0,1);(iii)sun for n=α to ∞|α_(n-1) α_n|<∞,sum from n=α|β_(n-1)-β_n|<∞设{x_n}_(n_1)~∞是由下式定义的迭代序列:{y_n=β_nx_n (1-β_n)Tx_n x_(n 1)=α_nu (1-α_n)y_n Then {x_n}_(n=1)~∞则{x_n}_(n=1)~∞强收敛于T的某不动点.     

关于有完全正规增长的准确零(R)级的整函数

设有一个由在复平面上绝对收敛的 Dirichlet 级数F(s)=(?)α_ne~(sλ)n(1)所表示的整函数,其中,s=σ it,0<λ_1<λ_2<…<λ_n…↑ ∞,(?)(logn/Kλ_nZ(λ_n))=0,(?)(logn/λ_n)<∞,α_n 是复数,σ及 t 是实变数.令 M(σ)=sup{|F(σ it)|,—∞相似文献   

关于平稳序列中心秩顺序统计量联合分布的稳定收敛性

§1.引言 设{ξ_n}是平稳序列,ξ_1~(n)≤ξ_2~(n)≤…≤ξ_n~(n)是ξ_1,…,ξ_n的顺序统计量,则称{ξ_(kn)~(n)}{ξ_n}的具有秩序列{k_n}的顺序统计量序列。记λ_n=k_n/n和?_n={nλ_n·(1-λ_n}~(1/2),如果min{k_n,n-k_n}→∞或等价地?_n→∞就称{k_n}为变秩序列。     

伪单调数列与带误差的凸组合迭代的收敛性

一 伪单调数列 定义1 设非负数列{ε_n}具有如下性质:“满足 a_(n+1)≤a_n+ε_n,n=1,2,… (1)且有下界的任意数列{a_n}必收敛”,则称数列{ε_n}具有“性质M”。 定理1 非负数列{ε_n}具有性质M的充要条件是级数sum from n=1 to ∞(ε_n)收敛。证 必要性:设非负数列{ε_n}具有性质M,取数列{a_(1n)}为     

一类两点边值问题的多重非负解

该文考虑两点边值问题[1/q(t)][q(t)y′(t)]′+p(t)f(y(t))= 0,λ_1 y(α)-λ_2y′(α)=0 and y(β)=B非负解的存在性, 其中p(t)可能在t=α或t=β附近具有奇异性, f(0)≥0, lim_(y→+∞)f(y)/y=+∞, 并且存在y>0, 使得f(y)<0.      

Immersions of spheres and algebraically constructible functions

Let Λ be an algebraic set and let (n is even) be a polynomial mapping such that for each there is r(λ) > 0 such that the mapping g _λ  =  g(· , λ) restricted to the sphere S ⁿ (r) is an immersion for every 0  <  r  <  r (λ), so that the intersection number I(g _λ|S ⁿ (r)) is defined. Then is an algebraically constructible function. I. Karolkiewicz and A. Nowel supported by the grant BW/5100-5-0286-7.     

Invariant equations defining coincident root loci

Let F(x) = xⁿ+₁ x^n-1+₂ x^n-2+ ··· +_n be a polynomial with complex coefficients, and suppose we are given a partition (₁,...,_r) of n. It is a classical problem to determine explicit algebraic conditions on the _i so that F may have roots with multiplicities ₁,...,_r. We give an invariant theoretic solution to this problem, to wit, we exhibit a set of covariants of F whose vanishing is a necessary and sufficient condition. The construction of such covariants is combinatorial, and involves associating a set of graphs on n vertices (called decisive graphs) to each .Received: 28 September 2003     

Nonexistence of single blow-up solutions for a nonlinear Schr?dinger equation involving critical Sobolev exponent

In this paper we shall consider the critical elliptic equation $ -\triangle u + \lambda a(x) u = u^{(N+2)/(N-2)}, \ \ x\in \Bbb R^N, \\ u > 0, \quad \int_{\Bbb R^N} |\nabla u|^2 \, dx < + \infty, \quad\quad (0.1)$ -\triangle u + \lambda a(x) u = u^{(N+2)/(N-2)}, \ \ x\in \Bbb R^N, \\ u > 0, \quad \int_{\Bbb R^N} |\nabla u|^2 \, dx < + \infty, \quad\quad (0.1) where $\lambda >0, N > 4$\lambda >0, N > 4 and a(x) is a real continuous, non negative function, not identically zero. By using a local Pohozaev identity, we show that problem (0.1) does not admit a family of solutions u_lu_\lambda which blows-up and concentrates as l? +￥\lambda \to +\infty at some zero point x₀ of a(x) if the order of flatness of the function a(x) at x₀ is b ? [2,N-4)\beta\in[2,N-4)     

What Is the Complexity of Stieltjes Integration?

We study the complexity of approximating the Stieltjes integral ∫¹₀ f(x) dg(x) for functions f having r continuous derivatives and functions g whose sth derivative has bounded variation. Let r(n) denote the nth minimal error attainable by approximations using at most n evaluations of f and g, and let comp(ε) denote the ε-complexity (the minimal cost of computing an ε-approximation). We show that r(n)≍n^{−min{r, s+1}} and that comp(ε)≍ε^{−1/min{r, s+1}}. We also present an algorithm that computes an ε-approximation at nearly minimal cost.     

Generalizations of Non-Commutative Neutrix Convolution Products of Functions

The non-commutative neutrix convolution product of the functions x ^r cos_–(x) and x ^s cos₊(x) is evaluated. Further similar non-commutative neutrix convolution products are evaluated and deduced.     

On the existence and nonexistence of global solutions for the porous medium equation with strongly nonlinear sources in a cone

In this paper, we study the initial-boundary value problem of the porous medium equation u _t  = Δu ^m  + V(x)u ^p in a cone D = (0, ∞) × Ω, where V(x) ~ (1 + |x|) ^σ . Let ω ₁ denote the smallest Dirichlet eigenvalue for the Laplace–Beltrami operator on Ω and let l denote the positive root of l ² + (n − 2)l = ω ₁. We prove that if m ≤ p ≤ m + (2 + σ)/(n + l), then the problem has no global nonnegative solutions for any nonnegative u ₀ unless u ₀ = 0; if p > m + (2 + σ)/n, then the problem has global solutions for some u ₀ ≥ 0.     

An Engel condition with generalized derivations on multilinear polynomials

Let R be a prime ring with extended centroid C, g a nonzero generalized derivation of R, f (x ₁,..., x _n) a multilinear polynomial over C, I a nonzero right ideal of R. If [g(f(r ₁,..., r _n)), f(r ₁,..., r _n)] = 0, for all r ₁, ..., r _n ∈ I, then either g(x) = ax, with (a − γ)I = 0 and a suitable γ ∈ C or there exists an idempotent element e ∈ soc(RC) such that IC = eRC and one of the following holds:

Strikte Konvexität für Variationsprobleme auf demn-dimensionalen Torus

We consider a variational problem with an integrandF:R ⁿ ×R×R ⁿ →R that isZ-periodic in the firstn+1 variables and satisfies certain growth-conditions. By a recent result of Moser, there exist for every α∈R ⁿ minimal solutionsu:R ⁿ →R minimising ƒF(x, u(x), u _x (x)) dx with respect to compactly supported variations ofu and such that sup |u(x)-αx|<∞. Given such a minimal solutionu we define the average action (whereB _r is ther-ball around 0∈R ⁿ ) and show thatM(α) is indeed independent of the minimal solutionu satisfying sup |u(x)-αx|<∞. We prove that this average actionM(α) is strictly convex in α.