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1.
Let KK be a nonempty closed convex subset of a Banach space EE, T:K→KT:KK a continuous pseudo-contractive mapping. Suppose that {αn}{αn} is a real sequence in [0,1][0,1] satisfying appropriate conditions; then for arbitrary x0∈Kx0K, the Mann type implicit iteration process {xn}{xn} given by xn=αnxn1+(1−αn)Txn,n≥0xn=αnxn1+(1αn)Txn,n0, strongly and weakly converges to a fixed point of TT, respectively.  相似文献   

2.
Let CC be a closed convex subset of a real Hilbert space HH and assume that TT is an asymptotically κκ-strict pseudo-contraction on CC with a fixed point, for some 0≤κ<10κ<1. Given an initial guess x0∈Cx0C and given also a real sequence {αn}{αn} in (0, 1), the modified Mann’s algorithm generates a sequence {xn}{xn} via the formula: xn+1=αnxn+(1−αn)Tnxnxn+1=αnxn+(1αn)Tnxn, n≥0n0. It is proved that if the control sequence {αn}{αn} is chosen so that κ+δ<αn<1−δκ+δ<αn<1δ for some δ∈(0,1)δ(0,1), then {xn}{xn} converges weakly to a fixed point of TT. We also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence.  相似文献   

3.
Let EE be a reflexive Banach space with a uniformly Gâteaux differentiable norm, let KK be a nonempty closed convex subset of EE, and let T:K?ET:K?E be a continuous pseudocontraction which satisfies the weakly inward condition. For f:K?Kf:K?K any contraction map on KK, and every nonempty closed convex and bounded subset of KK having the fixed point property for nonexpansive self-mappings, it is shown that the path x→xt,t∈[0,1)xxt,t[0,1), in KK, defined by xt=tTxt+(1−t)f(xt)xt=tTxt+(1t)f(xt) is continuous and strongly converges to the fixed point of TT, which is the unique solution of some co-variational inequality. If, in particular, TT is a Lipschitz pseudocontractive self-mapping of KK, it is also shown, under appropriate conditions on the sequences of real numbers {αn},{μn}{αn},{μn}, that the iteration process: z1∈Kz1K, zn+1=μn(αnTzn+(1−αn)zn)+(1−μn)f(zn),n∈Nzn+1=μn(αnTzn+(1αn)zn)+(1μn)f(zn),nN, strongly converges to the fixed point of TT, which is the unique solution of the same co-variational inequality. Our results propose viscosity approximation methods for Lipschitz pseudocontractions.  相似文献   

4.
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6.
We consider a multidimensional diffusion XX with drift coefficient b(Xt,α)b(Xt,α) and diffusion coefficient εa(Xt,β)εa(Xt,β) where αα and ββ are two unknown parameters, while εε is known. For a high frequency sample of observations of the diffusion at the time points k/nk/n, k=1,…,nk=1,,n, we propose a class of contrast functions and thus obtain estimators of (α,β)(α,β). The estimators are shown to be consistent and asymptotically normal when n→∞n and ε→0ε0 in such a way that ε−1n−ρε1nρ remains bounded for some ρ>0ρ>0. The main focus is on the construction of explicit contrast functions, but it is noted that the theory covers quadratic martingale estimating functions as a special case. In a simulation study we consider the finite sample behaviour and the applicability to a financial model of an estimator obtained from a simple explicit contrast function.  相似文献   

7.
We consider a multidimensional diffusion XX with drift coefficient b(α,Xt)b(α,Xt) and diffusion coefficient ?σ(β,Xt)?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔtk=kΔ for k=1…nk=1n on a fixed interval [0,T][0,T]. We study minimum contrast estimators derived from the Gaussian process approximating XX for small ??. We obtain consistent and asymptotically normal estimators of αα for fixed ΔΔ and ?→0?0 and of (α,β)(α,β) for Δ→0Δ0 and ?→0?0 without any condition linking ?? and ΔΔ. We compare the estimators obtained with various methods and for various magnitudes of ΔΔ and ?? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework.  相似文献   

8.
9.
Let KK be a compact convex subset of a real Hilbert space HH; T:K→KT:KK a hemicontractive map. Let {αn}{αn} be a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary x0∈Kx0K, the sequence {xn}{xn} defined iteratively by xn=αnxn1+(1−αn)Txnxn=αnxn1+(1αn)Txn, n≥1n1 converges strongly to a fixed point of TT.  相似文献   

10.
Let FFvFFv be the set of faulty nodes in an nn-dimensional folded hypercube FQnFQn with |FFv|≤n−2|FFv|n2. In this paper, we show that if n≥3n3, then every edge of FQn−FFvFQnFFv lies on a fault-free cycle of every even length from 44 to 2n−2|FFv|2n2|FFv|, and if n≥2n2 and nn is even, then every edge of FQn−FFvFQnFFv lies on a fault-free cycle of every odd length from n+1n+1 to 2n−2|FFv|−12n2|FFv|1.  相似文献   

11.
12.
In a rapidly growing population one expects that two individuals chosen at random from the nnth generation are unlikely to be closely related if nn is large. In this paper it is shown that for a broad class of rapidly growing populations this is not the case. For a Galton–Watson branching process with an offspring distribution {pj}{pj} such that p0=0p0=0 and ψ(x)=jpjI{jx}ψ(x)=jpjI{jx} is asymptotic to x−αL(x)xαL(x) as x→∞x where L(⋅)L() is slowly varying at ∞ and 0<α<10<α<1 (and hence the mean m=∑jpj=∞m=jpj=) it is shown that if XnXn is the generation number of the coalescence of the lines of descent backwards in time of two randomly chosen individuals from the nnth generation then n−XnnXn converges in distribution to a proper distribution supported by N={1,2,3,…}N={1,2,3,}. That is, in such a rapidly growing population coalescence occurs in the recent past rather than the remote past. We do show that if the offspring mean mm satisfies 1<m≡∑jpj<∞1<mjpj< and p0=0p0=0 then coalescence time XnXn does converge to a proper distribution as n→∞n, i.e., coalescence does take place in the remote past.  相似文献   

13.
Based on the classical Hermite spline interpolant H2n1H2n1, which is the piecewise interpolation polynomial of class Cn−1Cn1 and degree 2n−12n1, a piecewise interpolation polynomial H2nH2n of degree 2n2n is given. The formulas for computing H2nH2n by H2n1H2n1 and computing H2n+1H2n+1 by H2nH2n are shown. Thus a simple recursive method for the construction of the piecewise interpolation polynomial set {Hj}{Hj} is presented. The piecewise interpolation polynomial H2nH2n satisfies the same interpolation conditions as the interpolant H2n1H2n1, and is an optimal approximation of the interpolant H2n+1H2n+1. Some interesting properties are also proved.  相似文献   

14.
The dynamic behaviour of the one-dimensional family of maps f(x)=c2[(a−1)x+c1]−λ/(α−1)f(x)=c2[(a1)x+c1]λ/(α1) is examined, for representative values of the control parameters a,c1a,c1, c2c2 and λλ. The maps under consideration are of special interest, since they are solutions of the relaxed Newton method derivative being equal to a constant aa. The maps f(x)f(x) are also proved to be solutions of a non-linear differential equation with outstanding applications in the field of power electronics. The recurrent form of these maps, after excessive iterations, shows, in an xnxn versus λλ plot, an initial exponential decay followed by a bifurcation. The value of λλ at which this bifurcation takes place depends on the values of the parameters a,c1a,c1 and c2c2. This corresponds to a switch to an oscillatory behaviour with amplitudes of f(x)f(x) undergoing a period doubling. For values of aa higher than 1 and at higher values of λλ a reverse bifurcation occurs. The corresponding branches converge and a bleb is formed for values of the parameter c1c1 between 1 and 1.20. This behaviour is confirmed by calculating the corresponding Lyapunov exponents.  相似文献   

15.
In this paper, we consider Beta(2−α,α)(2α,α) (with 1<α<21<α<2) and related ΛΛ-coalescents. If T(n)T(n) denotes the length of a randomly chosen external branch of the nn-coalescent, we prove the convergence of nα−1T(n)nα1T(n) when nn tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ(n)σ(n) of collisions which occur in the nn-coalescent until the end of the chosen external branch, and for the block counting process associated with the nn-coalescent.  相似文献   

16.
Suppose XX is a real qq-uniformly smooth Banach space and F,K:X→XF,K:XX are Lipschitz ??-strongly accretive maps with D(K)=F(X)=XD(K)=F(X)=X. Let uu denote the unique solution of the Hammerstein equation u+KFu=0u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to uu. No invertibility assumption is imposed on KK and the operators KK and FF need not be defined on compact subsets of XX. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included.  相似文献   

17.
Let K(n,1)K(n,1) denote the minimal cardinality of a binary code of length nn and covering radius one. Fundamental for the theory of lower bounds for K(n,1)K(n,1) is the covering excess method introduced by Johnson and van Wee. Let δiδi denote the covering excess on a sphere of radius ii, 0≤i≤n0in. Generalizing an earlier result of van Wee, Habsieger and Honkala showed δp1≥p−1δp1p1 whenever n≡−1n1 (mod pp) for an odd prime pp and δ0=δ1=?=δp2=0δ0=δ1=?=δp2=0 holds. In the present paper we give the new estimation δp1≥(p−2)p−1δp1(p2)p1 instead. This answers a question of Habsieger and yields a “general improvement of the general excess bound” for binary codes with covering radius one. The proof uses a classification theorem for certain subset systems as well as new congruence properties for the δδ-function, which were conjectured by Habsieger.  相似文献   

18.
We prove that if GG is a finite simple group which is the unit group of a ring, then GG is isomorphic to: (a) a cyclic group of order 2; or (b) a cyclic group of prime order 2k−12k1 for some kk; or (c) a projective special linear group PSLn(F2)PSLn(F2) for some n≥3n3. Moreover, these groups do all occur as unit groups. We deduce this classification from a more general result, which holds for groups GG with no non-trivial normal 2-subgroup.  相似文献   

19.
Let XX be a uniformly smooth Banach space, CC be a closed convex subset of XX, and AA an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn}{xn} by the algorithm
xn+1=αnf(xn)+(1−αn)Jrnxn,xn+1=αnf(xn)+(1αn)Jrnxn,
where αnαn and γnγn are two sequences satisfying certain conditions, JrJr denotes the resolvent (I+rA)−1(I+rA)1 for r>0r>0, and f:C→Cf:CC be a fixed contractive mapping. Then as n→∞n, the sequence {xn}{xn} strongly converges to a point in F(A)F(A). The results presented extends and improves the corresponding results of Hong-Kun Xu [Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643].  相似文献   

20.
This paper considers the short- and long-memory linear processes with GARCH (1,1) noises. The functional limit distributions of the partial sum and the sample autocovariances are derived when the tail index αα is in (0,2)(0,2), equal to 2, and in (2,∞)(2,), respectively. The partial sum weakly converges to a functional of αα-stable process when α<2α<2 and converges to a functional of Brownian motion when α≥2α2. When the process is of short-memory and α<4α<4, the autocovariances converge to functionals of α/2α/2-stable processes; and if α≥4α4, they converge to functionals of Brownian motions. In contrast, when the process is of long-memory, depending on αα and ββ (the parameter that characterizes the long-memory), the autocovariances converge to either (i) functionals of α/2α/2-stable processes; (ii) Rosenblatt processes (indexed by ββ, 1/2<β<3/41/2<β<3/4); or (iii) functionals of Brownian motions. The rates of convergence in these limits depend on both the tail index αα and whether or not the linear process is short- or long-memory. Our weak convergence is established on the space of càdlàg functions on [0,1][0,1] with either (i) the J1J1 or the M1M1 topology (Skorokhod, 1956); or (ii) the weaker form SS topology (Jakubowski, 1997). Some statistical applications are also discussed.  相似文献   

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