共查询到10条相似文献，搜索用时 125 毫秒
1.
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
2.
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
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$
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
3.
Suppose that X is a complex Banach space with the norm ‖·‖ and n is a positive integer with dim X ⩾ n ⩾ 2. In this paper, we consider the generalized Roper-Suffridge extension operator $
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
on the domain $
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
$
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
defined by
|
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)(x) = {*{20}c}
{\sum\limits_{j = 1}^n {\left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)} ^{\beta _j } (f'(x_1^* (x)))^{\gamma _j } x_1^* (x)x_j } \\
{ + \left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)^{\beta _{n + 1} } (f'(x_1^* (x)))^{\gamma _{n + 1} } \left( {x - \sum\limits_{j = 1}^n {x_1^* (x)x_j } } \right)} \\
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)(x) = \begin{array}{*{20}c}
{\sum\limits_{j = 1}^n {\left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)} ^{\beta _j } (f'(x_1^* (x)))^{\gamma _j } x_1^* (x)x_j } \\
{ + \left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)^{\beta _{n + 1} } (f'(x_1^* (x)))^{\gamma _{n + 1} } \left( {x - \sum\limits_{j = 1}^n {x_1^* (x)x_j } } \right)} \\
\end{array}
相似文献
4.
We study k
th
order systems of two rational difference equations
|
$
x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - i} } }}
{{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }},n \in \mathbb{N},
$
x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - i} } }}
{{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }},n \in \mathbb{N},
相似文献
5.
k-Self-correcting circuits of functional elements in the basis { x
1& x
2, $
\bar x
$
\bar x
} are considered. It is assumed that constant faults on outputs of functional elements are of the same type. Inverters are
supposed to be reliable in service. The weight of each inverter is equal to 1. Conjunctors can be reliable in service, or
not reliable. Each reliable conjunctor implements a conjunction of two variables and has a weight p > k + 2. Each unreliable conjunctor implements a conjunction in its correct state and implements a Boolean constant δ ( δ ∈ {0, 1}) otherwise. Each unreliable conjunctor has the weight 1. It is stated that the complexity of realization of monotone
threshold symmetric functions $
f_2^n \left( {x_1 ,...,x_n } \right) = \mathop \vee \limits_{1 \leqslant i < j \leqslant n} x_1 x_j ,n = 3,4
$
f_2^n \left( {x_1 ,...,x_n } \right) = \mathop \vee \limits_{1 \leqslant i < j \leqslant n} x_1 x_j ,n = 3,4
, ... by such circuits asymptotically equals ( k + 3) n. 相似文献
6.
Let t ≥ 1, let A and B be finite, nonempty subsets of an abelian group G, and let $
A\mathop + \limits_i B
$
A\mathop + \limits_i B
denote all the elements c with at least i representations of the form c = a + b, with a ∈ A and b ∈ B. For |A|, |B| ≥ t, we show that either
|
$
\sum\limits_{i = 1}^t {|A\mathop + \limits_i B| \geqslant t|A| + t|B| - 2t^2 + 1,}
$
\sum\limits_{i = 1}^t {|A\mathop + \limits_i B| \geqslant t|A| + t|B| - 2t^2 + 1,}
相似文献
7.
For x = ( x 1, x 2, ..., x n ) ∈ ℝ + n , the symmetric function ψ n ( x, r) is defined by $\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } ,$\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } , 相似文献
8.
We study k
th
order systems of two rational difference equations
|
$
x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - 1} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - 1} } }}
{{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }}, y_n = \frac{{p + \sum\nolimits_{i = 1}^k {\delta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\varepsilon _i y_{n - i} } }}
{{q + \sum\nolimits_{j = 1}^k {D_j x_{n - j} + } \sum\nolimits_{j = 1}^k {E_j y_{n - j} } }} n \in \mathbb{N}
$
x_n = \frac{{\alpha + \sum\nolimits_{i = 1}^k {\beta _i x_{n - 1} + } \sum\nolimits_{i = 1}^k {\gamma _i y_{n - 1} } }}
{{A + \sum\nolimits_{j = 1}^k {B_j x_{n - j} + } \sum\nolimits_{j = 1}^k {C_j y_{n - j} } }}, y_n = \frac{{p + \sum\nolimits_{i = 1}^k {\delta _i x_{n - i} + } \sum\nolimits_{i = 1}^k {\varepsilon _i y_{n - i} } }}
{{q + \sum\nolimits_{j = 1}^k {D_j x_{n - j} + } \sum\nolimits_{j = 1}^k {E_j y_{n - j} } }} n \in \mathbb{N}
相似文献
9.
Abstract. Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces,the Ishikawa iteration 相似文献
10.
Let K be a square Cantor set, i.e., the Cartesian product K = E × E of two linear Cantor sets. Let δ
n
denote the proportion of the intervals removed in the nth stage of the construction of E. It is shown that if $
\delta _n = o(\frac{1}
{{\log \log n}})
$
\delta _n = o(\frac{1}
{{\log \log n}})
, then the corona theorem holds on the domain Ω = ℂ * \ K. 相似文献
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