共查询到20条相似文献,搜索用时 15 毫秒
1.
Suppose K is a closed convex nonexpansive retract of a real uniformly smooth Banach space E with P as the nonexpansive retraction. Suppose T : K → E is an asymptotically d-weakly contractive map with sequence {kn }, kn ≥ 1, lim kn = 1 and with F(T) n int (K) ≠ ø F(T):= {x ∈ K: Tx = x}. Suppose {x n } is iteratively defined by x n+1 = P((l ? knαn )x n +k n α n T(PT) n?l xn ), n = 1,2,...,x 1 ∈ K, where αn∈ (0,l) satisfies lim αn = 0 and Σαn = ∞. It is proved that {x n } converges strongly to some x * ∈ F(T)∩ int K. Furthermore, if K is a closed convex subset of an arbitrary real Banach space and T is, in addition uniformly continuous, with F(T) ≠ ø, it is proved that {xn } converges strongly to some x * ∈ F(T). 相似文献
2.
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
3.
非扩张映象不动点的迭代算法 总被引:2,自引:1,他引:1
设C是具有一致Gateaux可微范数的实Banach空间X中的一非空闭凸子集,T是C中不动点集F(T)≠0的一自映象.假设当t→0时,{Xt}强收敛到T的一不动点z,其中xt是C中满足对任给u∈C,xt=tu+(1-t)Txt的唯一确定元.设{αn},{βn}和{γn}是[0,1]中满足下列条件的三个实数列:(i)αn+βn+γn=1;(ii) limn-∞αn=0和.对任意的x0∈C,设序列{xn}定义为xn+1=αnu+βnxn+γnTxn,则{xn}强收敛到T的不动点. 相似文献
4.
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
(i) If the dual E* of E has the Kadec-Klee property then {x
n
} converges weakly to a common fixed point p ∈ F; (ii) If T satisfies condition (A′) then {x
n
} converges strongly to a common fixed point p ∈ F.
相似文献
5.
Let K be a nonempty closed convex subset of a real Banach space E and let be a uniformly continuous pseudocontraction. Fix any u∈K. Let {xn} be defined by the iterative process: x0∈K, xn+1:=μn(αnTxn+(1−αn)xn)+(1−μn)u. Let δ(?) denote the modulus of continuity of T with pseudo-inverse ?. If and {xn} are bounded then, under some mild conditions on the sequences n{αn} and n{μn}, the strong convergence of {xn} to a fixed point of T is proved. In the special case where T is Lipschitz, it is shown that the boundedness assumptions on and {xn} can be dispensed with. 相似文献
6.
C.E. Chidume 《Journal of Mathematical Analysis and Applications》2003,278(2):354-366
Let K be a nonempty closed convex and bounded subset of a real Banach space E and T:K→K be uniformly L-Lipschitzian, uniformly asymptotically regular with sequence {εn}, and asymptotically pseudocontractive with constant {kn}, where {kn} and {εn} satisfy certain mild conditions. Let a sequence {xn} be generated from x1∈K by xn+1:=(1−λn)xn+λnTnxn−λnθn(xn−x1), for all integers n?1, where {λn} and {θn} are real sequences satisfying appropriate conditions, then ‖xn−Txn‖→0 as n→∞. Moreover, if E is reflexive, and has uniform normal structure with coefficient N(E) and L<N(E)1/2 and has a uniformly Gâteaux differentiable norm, and T satisfies an additional mild condition, then {xn} also converges strongly to a fixed point of T. 相似文献
7.
Arif Rafiq 《Rendiconti del Circolo Matematico di Palermo》2011,60(3):455-461
Let K be a nonempty, closed and convex subset of a real Banach space E. Let T:K→K be a strictly pseudocontractive map. For a fixed x 0∈K, define a sequence {x n } by x n+1=(1?α n )x n +α n Tx n , where {α n } is a real sequence defined in [0,1] satisfying the following conditions (i) $\sum_{n=0}^{\infty }\alpha _{n}=\infty $ , (ii) lim? n→∞ α n =0. Then lim?inf? n→∞‖x n ?Tx n ‖=0. If, in addition, T is demicompact, then {x n } converges strongly to some fixed point of T. Remark 8 is important. 相似文献
8.
S. Thianwan 《Mathematical Notes》2011,89(3-4):397-407
Let X be a real uniformly convex Banach space and C a nonempty closed convex nonexpansive retract of X with P as a nonexpansive retraction. Let T 1, T 2: C → X be two uniformly L-Lipschitzian, generalized asymptotically quasi-nonexpansive non-self-mappings of C satisfying condition A′ with sequences {k n (i) } and {δ n (i) } ? [1, ∞),, i = 1, 2, respectively such that Σ n=1 ∞ (k n (i) ? 1) < ∞, Σ n=1 (i) δ n (i) < ∞, and F = F(T 1) ∩ F(T 2) ≠ ?. For an arbitrary x 1 ∈ C, let {x n } be the sequence in C defined by $$ \begin{gathered} y_n = P\left( {\left( {1 - \beta _n - \gamma _n } \right)x_n + \beta _n T_2 \left( {PT_2 } \right)^{n - 1} x_n + \gamma _n v_n } \right), \hfill \\ x_{n + 1} = P\left( {\left( {1 - \alpha _n - \lambda _n } \right)y_n + \alpha _n T_1 \left( {PT_1 } \right)^{n - 1} x_n + \lambda _n u_n } \right), n \geqslant 1, \hfill \\ \end{gathered} $$ where {α n }, {β n }, {γ n } and {λ n } are appropriate real sequences in [0, 1) such that Σ n=1 ∞ ] γ n < ∞, Σ n=1 ∞ λ n < ∞, and {u n }, }v n } are bounded sequences in C. Then {x n } and {y n } converge strongly to a common fixed point of T 1 and T 2 under suitable conditions. 相似文献
9.
10.
Let C be a closed, convex subset of a uniformly convex Banach space whose norm is uniformly Gâteaux differentiable and let T be an asymptotically nonexpansive mapping from C into itself such that the set F (T) of fixed points of T is nonempty. Let {an} be a sequence of real numbers with 0 £ an £ 10 \leq a_n \leq 1, and let x and x0 be elements of C. In this paper, we study the convergence of the sequence {xn} defined by¶¶xn+1=an x + (1-an) [1/(n+1)] ?j=0n Tj xn x_{n+1}=a_n x + (1-a_n) {1\over n+1} \sum\limits_{j=0}^n T^j x_n\quad for n=0,1,2,... . n=0,1,2,\dots \,. 相似文献
11.
C.E Chidume 《Journal of Mathematical Analysis and Applications》2004,296(2):410-421
Let K be a nonempty closed convex and bounded subset of a real Banach space E. Let be a strongly continuous uniformly asymptotically regular and uniformly L-Lipschitzian semi-group of asymptotically pseudocontractive mappings from K into K. Then for a given u∈K there exists a sequence {yn}∈K satisfying the equation yn=(1−αn)(T(tn))nyn+αnu for each , where αn∈(0,1) and tn>0 satisfy appropriate conditions. Suppose further that E is uniformly convex and has uniformly Gâteaux differentiable norm, under suitable conditions on the mappings T, the sequence {yn} converges strongly to a fixed point of . Furthermore, an explicit sequence {xn} generated from x1∈K by xn+1:=(1−λn)xn+λn(T(tn))nxn−λnθn(xn−x1) for all integers n?1, where {λn}, {θn} are positive real sequences satisfying appropriate conditions, converges strongly to a fixed point of . 相似文献
12.
Shin-ya Matsushita Wataru Takahashi 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1466-6030
Let C be a nonempty, closed and convex subset of a uniformly convex and smooth Banach space and let {Tn} be a family of mappings of C into itself such that the set of all common fixed points of {Tn} is nonempty. We consider a sequence {xn} generated by the hybrid method by generalized projection in mathematical programming. We give conditions on {Tn} under which {xn} converges strongly to a common fixed point of {Tn} and generalize the results given in [12], [14], [13] and [11]. 相似文献
13.
14.
Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space 总被引:1,自引:0,他引:1
E.U. Ofoedu 《Journal of Mathematical Analysis and Applications》2006,321(2):722-728
Let E be a real Banach space. Let K be a nonempty closed and convex subset of E, a uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {kn}n?0⊂[1,+∞), limn→∞kn=1 such that F(T)≠∅. Let {αn}n?0⊂[0,1] be such that ∑n?0αn=∞, and ∑n?0αn(kn−1)<∞. Suppose {xn}n?0 is iteratively defined by xn+1=(1−αn)xn+αnTnxn, n?0, and suppose there exists a strictly increasing continuous function , ?(0)=0 such that 〈Tnx−x∗,j(x−x∗)〉?kn‖x−x∗‖2−?(‖x−x∗‖), ∀x∈K. It is proved that {xn}n?0 converges strongly to x∗∈F(T). It is also proved that the sequence of iteration {xn} defined by xn+1=anxn+bnTnxn+cnun, n?0 (where {un}n?0 is a bounded sequence in K and {an}n?0, {bn}n?0, {cn}n?0 are sequences in [0,1] satisfying appropriate conditions) converges strongly to a fixed point of T. 相似文献
15.
Huang Jianfeng Wang Yuanheng 《高校应用数学学报(英文版)》2007,22(3):311-315
This paper studies the convergence of the sequence defined by x0∈C,xn 1=αnu (1-αn)Txn,n=0,1,2,…, where 0 ≤αn ≤ 1, limn→∞αn = 0, ∑∞n=0 αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results. 相似文献
16.
Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E^*, and C be a nonempty closed convex subset of E. Let {T(t) : t ≥ 0} be a nonexpansive semigroup on C such that F :=∩t≥0 Fix(T(t)) ≠ 0, and f : C → C be a fixed contractive mapping. If {αn}, {βn}, {an}, {bn}, {tn} satisfy certain appropriate conditions, then we suggest and analyze the two modified iterative processes as:{yn=αnxn+(1-αn)T(tn)xn,xn=βnf(xn)+(1-βn)yn
{u0∈C,vn=anun+(1-an)T(tn)un,un+1=bnf(un)+(1-bn)vn
We prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix(T(t)), which is a unique solution in F to the following variational inequality:
〈(I-f)q,j(q-u)〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 (2002)], and Kim and XU [Nonlear Analysis, 61, 51-60 (2005)] and Chen and He [Appl. Math. Lett., 20, 751-757 (2007)]. 相似文献
{u0∈C,vn=anun+(1-an)T(tn)un,un+1=bnf(un)+(1-bn)vn
We prove that the approximate solutions obtained from these methods converge strongly to q ∈∩t≥0 Fix(T(t)), which is a unique solution in F to the following variational inequality:
〈(I-f)q,j(q-u)〉≤0 u∈F Our results extend and improve the corresponding ones of Suzuki [Proc. Amer. Math. Soc., 131, 2133-2136 (2002)], and Kim and XU [Nonlear Analysis, 61, 51-60 (2005)] and Chen and He [Appl. Math. Lett., 20, 751-757 (2007)]. 相似文献
17.
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
18.
K. V. Storozhuk 《Siberian Mathematical Journal》2011,52(6):1104-1107
Let X be a Banach space and let T: X → X be a power bounded linear operator. Put X
0 = {x ∈ X ∣ T
n
x → 0}. Assume given a compact set K ⊂ X such that lim inf
n→∞
ρ{T
n
x, K} ≤ η < 1 for every x ∈ X, ∥x∥ ≤ 1. If $\eta < \tfrac{1}
{2}
$\eta < \tfrac{1}
{2}
, then codim X
0 < ∞. This is true in X reflexive for $\eta \in [\tfrac{1}
{2},1)
$\eta \in [\tfrac{1}
{2},1)
, but fails in the general case. 相似文献
19.
C.E. Chidume 《Journal of Mathematical Analysis and Applications》2003,282(2):756-765
Let E be a real uniformly smooth Banach space. Let A:D(A)=E→2E be an accretive operator that satisfies the range condition and A−1(0)≠∅. Let {λn} and {θn} be two real sequences satisfying appropriate conditions, and for z∈E arbitrary, let the sequence {xn} be generated from arbitrary x0∈E by xn+1=xn−λn(un+θn(xn−z)), un∈Axn, n?0. Assume that {un} is bounded. It is proved that {xn} converges strongly to some x∗∈A−1(0). Furthermore, if K is a nonempty closed convex subset of E and T:K→K is a bounded continuous pseudocontractive map with F(T):={Tx=x}≠∅, it is proved that for arbitrary z∈K, the sequence {xn} generated from x0∈K by xn+1=xn−λn((I−T)xn+θn(xn−z)), n?0, where {λn} and {θn} are real sequences satisfying appropriate conditions, converges strongly to a fixed point of T. 相似文献
20.
SupposeK is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach spaceE withP as a nonexpansive retraction. LetT 1,T 2 andT 3:K → E be nonexpansive mappings with nonempty common fixed points set. Letα n ,β n ,γ n ,α n ′ ,β n ′ ,γ n ′ ,α n ′′ ,β n ′′ andγ n ′′ be real sequences in [0, 1] such thatα n +β n +γ n =α n ′ +β n ′ +γ n ′ =α n ′′ +β n ′′ +γ n ′′ = 1, starting from arbitraryx 1 ∈ K, define the sequencex n by $$\left\{ \begin{gathered} z_n = P(\alpha ''_n T_1 x_n + \beta ''_n x_n + \gamma ''_n w_n ) \hfill \\ y_n = P(\alpha _n^\prime T_2 z_n + \beta _n^\prime x_n + \gamma _n^\prime v_n ) \hfill \\ x_{n + 1} = P(\alpha _n T_3 y_n + \beta _n x_n + \gamma _n u_n ) \hfill \\ \end{gathered} \right.$$ with the restrictions $\sum\limits_{n = 1}^\infty {\gamma _n }< \infty , \sum\limits_{n = 1}^\infty \gamma _n^\prime< \infty ,\sum\limits_{n = 1}^\infty {\gamma ''_n }< \infty $ . (i) If the dual E* ofE has the Kadec-Klee property, then weak convergence of ax n to somex* ∈ F(T 1) ∩F(T 2) ∩ (T 3) is proved; (ii) IfT 1,T2 andT 3 satisfy condition (A′), then strong convergence ofx n to some x* ∈F(T 1) ∩F(T 2) ∩ (T 3) is obtained. 相似文献