共查询到20条相似文献,搜索用时 31 毫秒
1.
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. 相似文献
2.
The Hausdorff Centred measure of the symmetry Cantor sets 总被引:1,自引:0,他引:1
Let 0<λ≤1/3,K (λ) be the attractor of an iterated function system { ψ1,ψ2 } on the line, where ψ1 (x ) =λx, ψ2(x)=1-λ+λx, x∈ [0,1]. We call K (λ) the symmetry Cantor sets. In this paper, we obtained the exact Hausdorff Centred measure of K (λ). 相似文献
3.
This paper considers thefinitary reconstruction of an ergodic measure preserving transformationT of a complete separable metric spaceX from a single trajectoryx, Tx, …, or more generally, from a suitable reconstruction sequence x=x
1,x
2, … withx
i∈X. Ann-sample reconstruction is a functionT
n: X
n+1 →X; the map
(·;x
1, …,x
n)is treated as an estimate ofT(·) based on then initial elements of x. Given a reference probability measureμ
0 and constantM>1, functionsT
1,T
2, … are defined, and it is shown that for everyμ with 1/M≤dμ/dμ
0≤M, everyμ-preserving transformationT, and every reconstruction sequence x forT, the estimates
(·;x
1, …,x
nconverge toT in the weak topology.
For the family of interval exchange transformations of [0, 1] a simple family of estimates is described and shown to be consistent
both pointwise and in the strong topology. However, it is also shown that no finitary estimation scheme is consistent in the
strong topology for the family of all ergodic Lebesgue measure preserving transformations of the unit interval, even if x
is assumed to be a generic trajectory ofT.
Supported in part by NSF Grant DMS-9501926. 相似文献
4.
Junmin Chen Lijuan Zhang Tiegang Fan 《Journal of Mathematical Analysis and Applications》2007,334(2):1450-1461
Viscosity approximation methods for nonexpansive mappings are studied. Consider the iteration process {xn}, where x0∈C is arbitrary and xn+1=αnf(xn)+(1−αn)SPC(xn−λnAxn), f is a contraction on C, S is a nonexpansive self-mapping of a closed convex subset C of a Hilbert space H. It is shown that {xn} converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality. 相似文献
5.
Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces 总被引:1,自引:0,他引:1
Giuseppe Marino 《Journal of Mathematical Analysis and Applications》2007,329(1):336-346
Let C be a closed convex subset of a real Hilbert space H and assume that T is a κ-strict pseudo-contraction on C with a fixed point, for some 0?κ<1. Given an initial guess x0∈C and given also a real sequence {αn} in (0,1). The Mann's algorithm generates a sequence {xn} by the formula: xn+1=αnxn+(1−αn)Txn, n?0. It is proved that if the control sequence {αn} is chosen so that κ<αn<1 and , then {xn} converges weakly to a fixed point of T. However this convergence is in general not strong. We then modify Mann's algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence. This result extends a recent result of Nakajo and Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379] from nonexpansive mappings to strict pseudo-contractions. 相似文献
6.
Motivated by a paper Chidume and Zegeye [Strong convergence theorems for common fixed points of uniformly L-Lipschitzian pseudocontractive semi-groups, Applicable Analysis, 86 (2007), 353–366], we prove several strong convergence theorems for a family (not necessarily a semigroup) ℱ = {T(t): t ∈ G} of nonexpansive or pseudocontractive non-self mappings in a reflexive strictly convex Banach space with a uniformly Gateaux differentiable norm, where G is an unbounded subset of ℝ+. Our results extend and improve the corresponding ones byMatsushita and Takahashi [Strong convergence theorems for nonexpansive
nonself-mappings without boundary conditions,Nonlinear Analysis, 68 (2008), 412–419],Morales and Jung [Convergence of paths for pseudo-contractive mappings in Banach spaces, Proceedings of American Mathematical Society, 128 (2000), 3411–3419], Song [Iterative approximation to common fixed points of a countable family of nonexpansive mappings,
Applicable Analysis, 86 (2007), 1329–1337], Song and Xu [Strong convergence theorems for nonexpansive semigroup in Banach spaces, Journal of Mathematical Analysis and Applications, 338 (2008), 152–161], Wong, Sahu, and Yao [Solving variational inequalities involving nonexpansive type mappings, Nonlinear Analysis, (2007) doi:10.1016/j.na. 2007.11.025] in the context of a non-semigroup family of non-self mappings.
相似文献
7.
Bao She Wei 《数学学报(英文版)》2002,18(4):701-718
In this paper, we consider certain mappings, ${\mathcal {M}}In this paper, we consider certain mappings, ℳ , sufficiently close to an integrable one, which is weakly reversible with
respct to the mappings ? sufficiently close to an involution of tye (m, n), where m, n∈Z
+ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for providing the existence
of a Cantor family of m-tori invariant under the reversible mappings ℳ and the reversing mapping ?.
Received September 29, 1999, Accepted July 18, 2000 相似文献
8.
Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces
S. Takahashi W. Takahashi M. Toyoda 《Journal of Optimization Theory and Applications》2010,147(1):27-41
Let C be a closed and convex subset of a real Hilbert space H. Let T be a nonexpansive mapping of C into itself, A be an α-inverse strongly-monotone mapping of C into H and let B be a maximal monotone operator on H, such that the domain of B is included in C. We introduce an iteration scheme of finding a point of F (T)∩(A+B)−10, where F (T) is the set of fixed points of T and (A+B)−10 is the set of zero points of A+B. Then, we prove a strong convergence theorem, which is different from the results of Halpern’s type. Using this result, we
get a strong convergence theorem for finding a common fixed point of two nonexpansive mappings in a Hilbert space. Further,
we consider the problem for finding a common element of the set of solutions of a mathematical model related to equilibrium
problems and the set of fixed points of a nonexpansive mapping. 相似文献
9.
10.
An operatorT defined on a subsetD(T) of a Banach spaceE and taking values in 2
E
is said to bem-accretive if for each λ>0, the mappingJ
λ=(I+λT)−1 is a single-valued nonexpansive mapping defined on all ofE. In this paper, facts derived from an elementary analysis of the bahavior of {J
λ
x}λ≧0 for fixedxεD(T) are applied to obtain theorems concerning existence of zeros and surjectivity.
Research supported in part by National Science Foundation grant: MCS 76-03945-A01. 相似文献
11.
In this paper, we introduce the hybrid method of modified Mann’s iteration for an asymptotically k-strict pseudo-contractive mapping. Then we prove that such a sequence converges strongly to PF(T)x0. This main theorem improves the result of Issara Inchan [I. Inchan, Strong convergence theorems of modified Mann iteration methods for asymptotically nonexpansive mappings in Hilbert spaces, Int. J. Math. Anal. 2 (23) (2008) 1135–1145] and concerns the result of Takahashi et al. [W. Takahashi, Y. Takeuchi, R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 341 (2008) 276–286], and many others. 相似文献
12.
We use viscosity approximation methods to obtain strong convergence to common fixed points of monotone mappings and a countable
family of nonexpansive mappings. Let C be a nonempty closed convex subset of a Hilbert space H and P
C
is a metric projection. We consider the iteration process {x
n
} of C defined by x
1 = x ∈ C is arbitrary and
$
x_{n + 1} = \alpha _n f(x_n ) + (1 - \alpha _n )S_n P_C (x_n + \lambda _n Ax_n )
$
x_{n + 1} = \alpha _n f(x_n ) + (1 - \alpha _n )S_n P_C (x_n + \lambda _n Ax_n )
相似文献
13.
Ruan Huojun Dai Meifeng Su Weiyi Dept. of Math. Zhejiang Univ. Hangzhou China. Dept. of Math. Jiangsu Univ. Zhenjiang China. Dept. of Math. Nanjing Univ. Nanjing China. 《高校应用数学学报(英文版)》2005,20(2):235-242
§ 1 IntroductionThe class of Cantor sets is a typical one of sets in fractal geometry.Mathematicianshave paid their attentions to such sets for a long time.Itis well known that the Hausdorffmeasure of the Cantor middle- third set is1(see[1]) .Recently,Feng[3] obtained the exactvalues of the packing measure for a class of linear Cantor sets.Using Feng s method,Zhuand Zhou[5] obtained the exactvalue of Hausdorff centred measure of the symmetry Cantorsets.In this papar,we consider the Ha… 相似文献
14.
On weak positive supercyclicity 总被引:1,自引:0,他引:1
A bounded linear operator T on a separable complex Banach space X is called weakly supercyclic if there exists a vector x ∈ X such that the projective orbit {λT
n
x: n ∈ ℕ λ ∈ ℂ} is weakly dense in X. Among other results, it is proved that an operator T such that σ
p
(T
*) = 0, is weakly supercyclic if and only if T is positive weakly supercyclic, that is, for every supercyclic vector x ∈ X, only considering the positive projective orbit: {rT
n
x: n ∈ ℂ, r ∈ ℝ+} we obtain a weakly dense subset in X. As a consequence it is established the existence of non-weakly supercyclic vectors (non-trivial) for positive operators
defined on an infinite dimensional separable complex Banach space. The paper is closed with concluding remarks and further
directions.
Partially supported by MEC MTM2006-09060 and MTM2006-15546, Junta de Andalucía FQM-257 and P06-FQM-02225.
Partially supported by Junta de Andalucía FQM-257, and P06-FQM-02225 相似文献
15.
Ettore Carletti 《Annali dell'Universita di Ferrara》1983,29(1):37-44
Riassunto Scopo di questo lavoro è dare una formula asintotica per il numero degli zeri di ReF
K(λ+it) e di ImF
K(λ+it), dove
eζ
K(8) è la funzione zeta di Dedekind associata al campo numericoK, con 0<t<T e λ numero reale fissato tale che 1−1/n<λ<1 doven è il grado diK.
Summary The aim of this paper is to give an asymptotic formula for the number of zeros of ReF K(λ+it) and ImF K(λ+it), where andζ K(8) is the Dedekind zeta function for a number fieldK, with 0<t<T and λ fixed real number such that 1−1/n<λ<1, wheren is the degree ofK.相似文献 16.
Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T
1, T
2 and T
3: K → E be asymptotically nonexpansive mappings with {k
n
}, {l
n
} and {j
n
}. [1, ∞) such that Σ
n=1
∞
(k
n
− 1) < ∞, Σ
n=1
∞
(l
n
− 1) < ∞ and Σ
n=1
∞
(j
n
− 1) < ∞, respectively and F nonempty, where F = {x ∈ K: T
1x
= T
2x
= T
3
x} = x} denotes the common fixed points set of T
1, T
2 and T
3. Let {α
n
}, {α′
n
} and {α″
n
} be real sequences in (0, 1) and ∈ ≤ {α
n
}, {α′
n
}, {α″
n
} ≤ 1 − ∈ for all n ∈ N and some ∈ > 0. Starting from arbitrary x
1 ∈ K define the sequence {x
n
} by
17.
D. de Werra 《Mathematical Programming》1984,30(3):261-266
A polyhedronP = {x∈ ℝ
+
n
∣d ⩽Ax ⩽e} is said to have the real decomposition property (RDP) if for any positiveT and any realx∈TP, there are positive coefficients λ1,…, λ
r
and integers
1, …,s
r
∈P withx = λ
l
s
l
+ … + λ
r
s
r
andT=λ
l
+ ⋯ + λ
r
. We give a constructive proof that this property holds for a polyhedronP iffP is integral. This construction is used to show that some classes of polyhedra have an integral decomposition property. Furthemore,
the RDP provides a generalization of the theorem of Birkhoff-von Neumann. So RDP may be used in some scheduling problems on
parallel processors with preemptions. 相似文献
18.
Paul-Emile Maing 《Journal of Approximation Theory》2006,140(2):127-140
This paper deals with the general iteration method , for calculating a particular zero of A, an m-accretive operator in a Banach space X, Tn being a sequence of nonexpansive self-mappings in X. Under suitable conditions on the parameters and X, we state strong and weak convergence results of (xn). We also show how to compute a common zero of two m-accretive operators in X. 相似文献
19.
20.
Andrés del Junco 《Israel Journal of Mathematics》1983,44(2):160-188
LetT
α be the translationx↦x+α (mod 1) of [0, 1), α irrational. LetT be the Lebesgue measure-preserving automorphism ofX=[0, 3/2) defined byTx = x + 1 forx∈[0, 1/2),Tx=T
α(x−1) forx∈[1,3/2) andTx = T
α
x forx∈[1/2, 1), i.e.T isT
α with a tower of height one built over [0, 1/2). If α is poorly approximable by rationals (there does not exist {p
n
/q
n
} with |α−p
n
/q
n
|=o(q
n
−2)) and λ is a measure onX
k
all of whose one-dimensional marginals are Lebesgue and which is ⊗
i − 1
k
T
1 invariant and ergodic (l>0) then λ is a product of off-diagonal measures. This property suffices for many purposes of counterexample construction.
A connection is established with the POD (proximal orbit dense) condition in topological dynamics.
Research supported in part by NSF contract MCS-8003038. 相似文献
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