共查询到20条相似文献,搜索用时 125 毫秒
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关于非扩张映象的不动点逼近的Ishikawa迭代程序 总被引:5,自引:1,他引:4
设E是一致凸Banach空间,满足Opial条件或具有Frechet可微范数.又设C是E的有界闭凸子集.若T:C→C是非扩张映象,则对任给的初始数据x0∈C,由Ishikawa迭代程序xn+1=tnT(snTxn+(1-sn)xn)+(1-tn)xn,n≥0,定义的序列{xn}弱收敛到T的 相似文献
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对x = (x1, x2,···, xn) ∈ (0,1)n 和 r ∈ {1, 2,···, n} 定义对称函数
Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1∑j=1r(1+xi3/1- xi3)1/r,
其中i1, i2, ···, ir 是整数. 该文证明了Fn(x, r) 是(0,1)n 上的Schur凸、Schur乘性凸和Schur调和凸函数. 作为应用,利用控制理论建立了若干不等式. 相似文献
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在1965年,Djokoviě,D.Z提出[1]:设x01<…n是n+1个实数. 相似文献
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对称链是一种特殊的偏序,用它已经得到了许多非常漂亮的结果.如果一个偏序集可以分解成不相交的对称链之并,则称此偏序集具有对称链分解.但目前已证明具有这种分解的偏序集并不多.L(m,n)={(x1,x2,…,xn)|xi均为整数且0≤x1≤x2≤…≤xm≤n},序关系≤定义为:X=(x1,x2,…,xm< 相似文献
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Let X be a Banach space, (xn, Fn, n<- 1) a X-valued adapted sequence on probability space (Q, F, P) . Let T be all stopping times with respect to(Fn,n < - 1) . (xn, Fn,n< - 1) is called a T- uniform amart if there exists a t0∈T such that for each t∈T with t0,E‖xt‖<∞ and if (?)=0.In this paper we prove that. 相似文献
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Let φ(x1,x2,…xm) be a real Borel measurable symmetrical function of the m variables, and let Un denote the U-statistic with kernel φ. In this note it is proved that the necessary and sufficient condition for E|φ|<+∞ is that there exists an n≥m such that E|Un|< + ∞. 相似文献
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本文给出对称多项式的幂的Schur函数展式(x1k+…+xnk)m=sumC(λ1,…,λn)S(λ1,…,λn)(x1,…,xn)中系数C(λ1,…,λn)的计算方法,并把它和文献[1]应用于计数几何的若干问题。 相似文献
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本文推广了Peterson和Taft的主要结果.主要证明了F[x1,x2,… ,xn]0与所有n元线性递归序列组成的集合是1-1对应的.从而可赋予后者一个Hopf代数结构.这样对研究多元线性递归序列内的运算性质(如Hurwitz与Hadamard乘法)提供了方便.此外还进一步研究了线性递归序列的解空间理论.并证明了n元线性递归序列的解空间由一个线性齐次偏微分方程组唯一确定. 相似文献
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This paper is to solve several problems on the global attractivity of the zero solution of the nonautonomous difference equation xn+1 - xn + Pnxn-kn = 0,n ∈ Z(0), where {Pn} is a sequence of nonnegative real numbers, and {kn} is a sequence of nonnegative integers with n - kn→∞ as n→∞. 相似文献
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非线性时滞差分议程的全局渐近稳定性 总被引:1,自引:0,他引:1
In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained,xn 1=xn xn-1xn-2 a/xmxm-1 xn-2 a,n=0,1…,where a∈(0,∞) and the initial values x-2,x-1,x0∈(0,∞).As a special case,a conjecture by Ladas is confirmed. 相似文献
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高怀毅 《高等学校计算数学学报》2004,26(4):314-326
The King-Werner iteration xn 1= xn -F‘(1/2(xn yn))^-1 F(xn);yn 1=xn 1-F‘(1/2(xn yn))^-1F(xn 1) which is used for solving the operator eqution in Banach space F(x) = 0 requires the inverse of the opterator‘s derivative.Now in this paper a deformation King-Werner method without use of inverse is presented and the convergence of this method is proved with the skill of the majoring function. In addition, for the existed convergent theorem the convergent condtions are amended. The corresponding convergence theorem holds also with the amended conditions and its error bounds is obtained. At last a midpoint method of order 1 √2 : yn=xn-F‘(xn)^-1F(xn);xn 1=xn-F‘(xn yn/2)^-1F(xn) which is studied by D.Chen and I.K.Argros is convergent withby milder conditions by recurence relations. 相似文献
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研究了一个呼吸动力学时滞微分方程模型.x(t)=1-αx(t)xn(t-τ)1+xn(t-τ).通过利用一种映射方法得到了该系统平衡点全局吸引的充分条件.所得结论优于已有的结果. 相似文献
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设E是实的一致凸Banach空间,K是E的一个非空闭凸集,P是E到K上的非扩张的保核收缩映射.设T1,T2,T3:K→E分别是具有数列{hn},{ln},{kn}[1,∞)的渐近非扩张非自映射,使得sum (hn-1) from n=1 to ∞<∞,sum ((ln-1)) from n=1 to ∞<∞及sum (n=1(kn-1) from n=1 to ∞<∞,且F=F(T1)∩F(T2)∩F(T3)={x∈K:T1x=T2x=T3x}≠Ф.定义迭代序列{xn}:x1∈K,xn+1=P((1-αn)xn+αnT1(PT1)n-1yn),yn=P((1-βn)xn+βnT2(PT2)n-1zn),zn=P((1-γn)xn+γnT3(PT3)n-1xn),其中{αn},{βn},{γn}[ε,1-ε],ε是大于零的实数.(i)如果T1,T2,T3中有一个是全连续的或者半紧的,则{xn}强收敛于某一点q∈F;(ii)如果E具有Frechet可微范数或者满足Opial’s条件或者E的对偶空间E~*具有Kadec-Klee性质,则{xn}弱收敛于某一点q∈F. 相似文献
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侯成敏 《数学的实践与认识》2007,37(18):180-183
研究了差分方程xn+1=(a+bxn)/(A+B xn-k)(C+D xn-l),n=0,1,2,….其中a,b,A,B,C∈(0,∞),D∈[0,∞),k,l是正整数,初值条件x-k,…,x-1及x0是任意正常数的全局吸引性,推广了相关文献的相关结果. 相似文献
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An oscillation criterion is obtained for even order neutral type differenceequations of the following formΔ~m(x_n+α_nx_(n-т))+f(n,x_n,x_(n-σ))=0,n=n_0,n_0+1,…,where m≥2 is even, n_0 is a nonnegative integer, Δ is the forward differenceoperator defined by Δx_n=x_(n+1)-x_n, and for i≥1, Δ~i is the i~(th)-order forwarddifference operator defined by Δ~ix_n=Δ(Δ~(i-1)x_n),т and σ are positive integers. 相似文献
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<正>In this paper you will learn the basic integration rule from the basic differentiation rule.Last time we have learned anti-derivative,indefinite integral,and the power rule in integration.Let us recall what the power rule in differentiation is.If n is a real number,and y=xn,then y'=nxn-1.Proof:Let y=xn,we get ln|y|=ln|xn|,Since ln|xn|=n ln|x|,so we get ln|y|=n ln|x|.Take differentiation for both side above:y'y=n x. 相似文献