共查询到20条相似文献,搜索用时 140 毫秒
1.
Liu Chuan ZENG 《数学学报(英文版)》2006,22(2):407-416
Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt : t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F(T) of T in C is nonempty. It is shown that if G is right reversible, then for each almost-orbit u(.) of T, ∩s∈G ^-CO{u(t) : t ≥ s} ∩ F(T) consists of at most one point. Furthermore, ∩s∈G ^-CO{Ttx : t ≥ s} ∩ F(T) is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F(T) such that PTs - TsP = P for all s ∈ G and Px ∈^-CO{Ttx : s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u(t) : t ∈ G} to a common fixed point of T. 相似文献
2.
Let X be a Banach space with a weakly continuous duality map Jφ,C a non-empty weakly compact convex subset of X, and T:(T(t):t∈S} an asymptotically nonexpansive type semigroup on C. In this paper, the inequality K∩F(T)≠0 is characterized, where K is a subset of C and F(T) is the set of all common fixed points of T. Furthermore, it is shown that an almost-orbit {u(t):t∈S} of T converges weakly to a point in F(T) if and only if {u(t):t∈S}is weakly asymptotically regular. 相似文献
3.
Let C be a nonempty closed convex subset of a real Banach space E. Let S : C→ C be a quasi-nonexpansive mapping, let T : C→C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F := {x ∈C : Sx = x and Tx = x}≠Ф Let {xn}n≥0 be the sequence generated irom an arbitrary x0∈Cby xn+i=(1-cn)Sxn+cnT^nxn, n≥0.We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence {xn} to an element of F. These extend and improve the recent results of Moore and Nnoli. 相似文献
4.
Let X be a Banach space with a weakly continuous duality map Jψ, C a non-empty weakly compact convex subset of X, and T = (T(t) : t ∈ S} an asymptotically nonexpansive type semigroup on C. In this paper, the inequality K ∩ F(T) ≠ (?) is characterized, where K is a subset of C and F(T) is the set of all common fixed points of T. Furthermore, it is shown that an almost-orbit 相似文献
5.
On Well-posed Mutually Nearest and
Mutually Furthest Point Problems in Banach Spaces 总被引:3,自引:0,他引:3
ChongLI RenXingNI 《数学学报(英文版)》2004,20(1):147-156
Let G be a non-empty closed(resp.bounded closed)boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X.Let K(X)denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance.Moreover,let KG(X)denote the closure of the set {A∈K(x):A∩G=0}.We prove that the set of all A∈KG(X)(resp.A∈K(X)),such that the minimization (resp.maximization)problem min(A,G)(resp.max(A,G))is well posed,contains a dense Gδ-subset of KG(X)(resp.K(X)).thus extending the recent results due to Blasi,Myjak and Papini and Li. 相似文献
6.
Kazuhide NAKAJO 《数学物理学报(B辑英文版)》2017,37(2):342-354
Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {A_n}_(n∈N) be a family of monotone and Lipschitz continuos mappings of C into E~*. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [10] for solving the variational inequality problem for{A_n} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space. 相似文献
7.
Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectively by {a,b,c}-ntype and {a,b,c}-ctype. We proved the following: 1. If T is {a,b,c}-ntype mapping, then inf{ || T(x)-x|| :x C C} =0, accordingly T has a unique fixed point. Moreover, any sequence {Xn}n∈NN in C with limn→∞||T(xn) - Xn|| = 0 has a subsequence strongly convergent to the unique fixed point of T. 2. If T is {a,b,c}-ctype mapping, then T has a unique fixed point. Moreover, for any x∈C the sequence of iterates {Tn (x)}n∈N has subsequence strongly convergent to the unique fixed point of T. This paper extends and generalizes some of the results given in [2,4, 7] and [13]. 相似文献
8.
Lei YANG 《数学学报(英文版)》2022,(1):205-224
Let X = G/Γ be a homogeneous space with ambient group G containing the group H =(SO(n, 1))k and x ∈ X be such that Hx is dense in X. Given an analytic curve ? : I = [a, b] → H,we will show that if φ satisfies certain geometric condition, then for a typical diagonal subgroup A ={a(t) : t ∈ R} ? H the translates {a(t)?(I)x : t > 0} of the curve ?(I)x will tend to be equidistributed in X as t → +∞. The proof is based on Ratner’s theorem and linearization technique. 相似文献
9.
Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields
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Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields. 相似文献
10.
Let X = {X(t),t <σ} (σ is lifespan) be a birth and death process with explosion whose characteristic triple (Mα,MC,MD) of MX in terms of (α, C, D) and M. This means that a lot of given birth and death processes can be embedded in one and the same birth and death process. If κ∈ E and M = {κ},we decompose X into κX, κ∈ E. 相似文献
11.
§1.IntroductionLetHbeaHilbertspacewithnorm‖·‖andinnerproduct(·,·)andletCbeanonemptysubsetofH.AmappingT:C|→CissaidtobeLipschit... 相似文献
12.
Fixed Point Theorem of $\{a,b,c\}$ Contraction and Nonexpansive Type Mappings in Weakly Cauchy Normed Spaces
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Let $C$ be a closed convex weakly Cauchy subset of a normed space $X$. Then we define a new $\{a,b,c\}$ type nonexpansive and $\{a,b,c\}$ type contraction mapping $T$ from $C$ into $C$. These types of mappings will be denoted respectively by $\{a,b,c\}$-$n$type and $\{a,b,c\}$-$c$type. We proved the following:1. If $T$ is $\{a,b,c\}$-$n$type mapping, then $\inf\{\|T(x)-x\|:x\in C\}=0$, accordingly $T$ has a unique fixed point. Moreover, any sequence $\{x_{n}\}_{n\in \mathcal{N}}$ in $C$ with $\lim_{n\to \infty}\|T(x_{n})-x_{n}\|=0$ has a subsequence strongly convergent to the unique fixed point of $T$.2. If $T$ is $\{a,b,c\}$-$c$type mapping, then $T$ has a unique fixed point. Moreover, for any $x\in C$ the sequence of iterates $\{T^{n}(x)\}_{n\in \mathcal{N}}$ has subsequence strongly convergent to the unique fixed point of $T$.This paper extends and generalizes some of the results given in [2,4,7] and [13]. 相似文献
13.
14.
Green's Equivalences on Semigroups of Transformations Preserving Order and an Equivalence Relation 总被引:4,自引:0,他引:4
Let ${\cal T}_X$ be the full transformation semigroup on the set $X$,
\[
T_{E}(X)=\{f\in {\cal T}_X\colon \ \forall(a,b)\in E,(f(a),f(b))\in E\}
\]
be the subsemigroup of ${\cal T}_X$ determined by an equivalence
$E$ on $X$. In this paper the set $X$ under consideration is a
totally ordered set with $mn$ points where $m\geq 2$ and $n\geq
3$. The equivalence $E$ has $m$ classes each of which contains $n$
consecutive points. The set of all order preserving
transformations in $T_{E}(X)$ forms a subsemigroup of $T_E(X)$
denoted by
\[
{\cal O}_{E}(X)=\{f\in T_{E}(X)\colon \ \forall\, x, y\in X, \ x\leq
y \mbox{ implies } f(x)\leq f(y)\}.
\]
The nature of regular elements in ${\cal O}_{E}(X)$ is described
and the Green's equivalences on ${\cal O}_{E}(X)$ are
characterized completely. 相似文献
15.
Qi Guo 《Discrete and Computational Geometry》2005,34(2):351-362
Given a convex body $C\subset R^n$ (i.e., a compact convex set with nonempty
interior), for $x\in$ {\it int}$(C)$, the interior, and a hyperplane $H$ with $x\in H$,
let $H_1,H_2$ be the two support hyperplanes of $C$ parallel to $H$. Let $r(H, x)$
be the ratio, not less than 1, in which $H$ divides the distance between
$H_1,H_2$. Then the quantity
$${\it As}(C):=\inf_{x\in {\it int}(C)}\,\sup_{H\ni x}\,r(H,x)$$
is called the Minkowski measure of asymmetry of $C$. {\it As}$(\cdot)$ can be viewed as a real-valued function defined on the family of
all convex bodies in $R^n$. It has been known for a long time that {\it As}$(\cdot)$
attains its minimum value 1 at all centrally symmetric convex bodies and maximum
value $n$ at all simplexes. In this paper we discuss the stability of the
Minkowski measure of asymmetry for convex bodies. We give an estimate for the
deviation of a convex body from a simplex if the corresponding Minkowski measure
of asymmetry is close to its maximum value. More precisely, the following result
is obtained: Let $C\subset R^n$ be a convex body. If {\it As}$(C)\ge n-\varepsilon$ for some $0\le
\varepsilon < 1/8(n+1),$ then there exists a simplex $S_0$ formed by $n+1$
support hyperplanes of $C$, such that
$$(1+8(n+1)\varepsilon)^{-1}S_0\subset C\subset S_0,$$
where the homethety center is the (unique) Minkowski critical point of $C$. So
$$d_{{\rm BM}}(C,S)\le 1+8(n+1)\varepsilon$$
holds for all simplexes $S$, where $d_{{\rm BM}}(\cdot,\cdot)$ denotes the Banach-Mazur distance. 相似文献
16.
设X是齐型空间.设T_(j,1)和T_(j,2)是具有非光滑核的奇异积分算子,或者是±II(I是恒等算子).令Toeplitz型算子T_b=■T_(j,1)M_T_(j,2),其中M_bf(x)=b(x)f(x).研究了当b∈BMO(X)时,T_b(f)在加权情况下的有界性,以及当b∈BMO(X)时,与经典Carderon-Zygmund算子相联的T_b(f)在Morrey空间上的有界性. 相似文献
17.
18.
令A是阿贝尔范畴, T是A的一个自正交子范畴, 且T中每个对象均有有限投射维数和内射维数. 假设左Gorenstein子范畴lG(T)等于T的右正交类,且右Gorenstein子范畴rG(T)等于T的左正交类,我们证明了Gorenstein子范畴$G(T)$等于T的左正交类与T的右正交类之交,并且证明了它们的稳定范畴三角等价于A关于T的相对奇点范畴.作为应用,令$R$是有有限左自内射维数的左诺特环, $_RC_s$是半对偶化双模,且所有内射左$R$-模的平坦维数的上确界有限, 我们证明了 若$\mbox{}_RC$有有限内射(平坦)维数且$C$的右正交类包含$R$,则存在从$C$-Gorenstein投射模与关于$C$的Bass类的交到关于$C$-投射模的相对奇点范畴间的三角等价,推广了某些经典的结果. 相似文献
19.
Numerical Algorithms - Let $\displaystyle \{x_{k,n-1}\}_{k=1}^{n-1}$ and $\displaystyle \{x_{k,n}\}_{k=1}^{n},$ $n \in \mathbb {N}$ , be two sets of real, distinct points satisfying the interlacing... 相似文献
20.
Fatemah Ayatollah Zadeh Shirazi Amir Fallahpour Mohammad Reza Mardanbeigi & Zahra Nili Ahmadabadi 《分析论及其应用》2022,38(1):110-120
For a finite discrete topological space $X$ with at least two elements, a nonempty set $\Gamma$, and a map $\varphi:\Gamma \to \Gamma$, $\sigma_{\varphi}:X^{\Gamma} \to X^{\Gamma}$with $\sigma_{\varphi}((x_{\alpha})_{\alpha \in \Gamma})=(x_{\varphi(\alpha)})_{\alpha \in \Gamma}$ (for $(x_{\alpha})_{\alpha \in \Gamma} \in X^{\Gamma}$) is a generalized shift. In this text for $\mathcal{S} = \{\sigma_{\varphi}:\varphi \in \Gamma^{\Gamma}\}$ and $\mathcal{H}=\{\sigma_{\varphi}:\Gamma \xrightarrow{\varphi} \Gamma$ is bijective$\}$ we study proximal relations of transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$. Regarding proximal relation we prove: $$P(\mathcal{S}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \exists \beta \in \Gamma (x_{\beta} = y_{\beta})\}$$and $P(\mathcal{H}, X^{\Gamma} ) \subseteq \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\beta \in \Gamma : x_{\beta} = y_{\beta}\}$ is infinite$\}$ $\cup\{($ $x,x) : x \in \mathcal{X}\}$. Moreover, for infinite $\Gamma$, both transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$ are regionally proximal, i.e., $Q(\mathcal{S}, X^{\Gamma}) = Q(\mathcal{H}, X^{\Gamma} ) = X^{\Gamma} \times X^{\Gamma}$, also for sydetically proximal relation we have $L(\mathcal{H}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\gamma ∈ \Gamma :$ $x_{\gamma} \neq y_{\gamma}\}$ is finite$\}$. 相似文献