共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we propose three different kinds of iteration schemes to compute the approximate solutions of variational inequalities in the setting of Banach spaces. First, we suggest Mann-type steepest-descent iterative algorithm, which is based on two well-known methods: Mann iterative method and steepest-descent method. Second, we introduce modified hybrid steepest-descent iterative algorithm. Third, we propose modified hybrid steepest-descent iterative algorithm by using the resolvent operator. For the first two cases, we prove the convergence of sequences generated by the proposed algorithms to a solution of a variational inequality in the setting of Banach spaces. For the third case, we prove the convergence of the iterative sequence generated by the proposed algorithm to a zero of an operator, which is also a solution of a variational inequality. 相似文献
2.
Assume that F is a nonlinear operator on a real Hilbert space H which is -strongly monotone and -Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed point sets of a finite number of nonexpansive mappings on H. We devise an iterative algorithm which generates a sequence (x
n
) from an arbitrary initial point x
0H. The sequence (x
n
) is shown to converge in norm to the unique solution u* of the variational inequality
Applications to constrained pseudoinverse are included. 相似文献
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本文的目的是在Hilbert空间中引入和研究了一种新的迭代序列,用以寻求具逆一强单调映象的广义平衡问题的解集与无限簇非扩张映象的不动点集的公共元.在适当的条件下,用黏性逼近法证明了逼近于这一公共元的强收敛定理.应用该结论,我们证明了逼近于平衡问题和变分不等式问题的强收敛定理.所得结果改进和推广了文献的相应结果. 相似文献
5.
引入一个用于寻求带扰动映像的广义平衡问题解集以及可数无穷多非扩张映像之族公共不动点集的公共解的新的迭代算法.
证明了由此算法生成的序列的强收敛性. 所得的结果推广改进了先前许多作者的结果. 相似文献
6.
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings. The main results obtained in this paper improve and extend some recent results. 相似文献
7.
Maryam Yazdi & Saeed Hashemi Sababe 《计算数学(英文版)》2023,41(1):153-172
In this paper, we introduce a new iterative method based on the hybrid viscosity approximation method for finding a common element of the set of solutions of a general system of variational inequalities, an equilibrium problem, and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space. We prove a strong convergence theorem of the proposed iterative scheme under some suitable conditions on the parameters. Furthermore, we apply our main result for W-mappings. Finally, we give two numerical results to show the consistency and accuracy of the scheme. 相似文献
8.
Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities 总被引:3,自引:0,他引:3
Assume that F is a nonlinear operator on a real Hilbert space H which is η-strongly monotone and κ-Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on H. We construct an iterative algorithm with variable parameters which generates a sequence {x
n
} from an arbitrary initial point x
0 ∊ H. The sequence {x
n
} is shown to converge in norm to the unique solution u
∗ of the variational inequality
The authors thank the referees for helpful comments and suggestions
His research was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education
Institutions of MOE, China and the Dawn Program Foundation in Shanghai
His research was partially supported by grant from the National Science Council of Taiwan
His research was partially supported by grant from the National Science Council of Taiwan 相似文献
9.
Based on some iteration schemes, we study the viscosity approximation results for multivalued nonexpansive mappings in Hilbert space and Banach space. For that mapping, we obtain a fixed point to solve its related variational inequality. 相似文献
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在具有一致Gateaux可微范数的Banach空间中,研究了一个逼近非扩张映射不动点的粘性逼近方法,运用Banach极限推导了该逼近方法收敛的充分条件,并通过对该粘性逼近方法的修正逐步减少了收敛分析中的限制条件. 相似文献
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主要在自反和严格凸的且具有一致G(a)teaux可微范数的Banach空间中研究了非扩张非自映射的粘滞迭代逼近过程,证明了此映射的隐格式与显格式粘滞迭代序列均强收敛到它的某个不动点. 相似文献
14.
增生算子粘性逼近的强收敛定理 总被引:1,自引:0,他引:1
假设$E$为实Banach空间, $A$为具有零点的增生算子. 定义序列 $\{x_n\}$如下: $x_{n+1}=\alpha_n f(x_n)+(1-\alpha_n)J_{r_n}x_n$, 这里$\{\alpha_n\}$, $\{r_n\}$ 满足一定条件的序列, 令$J_r=(I+rA)^{-1}$, $r>1$. 假如空间$E$有弱连续对偶映像,或者$E$为一致光滑的,均得到了序列 $\{x_n\}$的强收敛性结果. 相似文献
15.
唐艳 《数学的实践与认识》2013,43(6)
在具有一致Gateaux可微范数的Banach空间中,建立了一个改进的非扩张映射不动点的粘性逼近方法,并在一定条件下证明了该方法所得到的迭代序列的强收性.本文所得结果扩展并统一了部分文献的结果. 相似文献
16.
在H illbert空间和Banach空间中,通过隐粘性迭代方法和显粘性逼近方法,证明了非扩张半群公共不动点的强收敛定理.所得结论改进和扩展了近期的相关结果. 相似文献
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18.
Let K be a nonempty closed and convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping J. Let T: K → K be a multivalued non-expansive non-self-mapping satisfying the weakly inwardness condition as well as the condition T(y) = {y} for any y ∈ F(T) and such that for a contraction f: K → K and any t ∈ (0, 1), there exists x t ∈ K satisfying x t ∈ tf(x t ) + (1 ? t)Tx t . Then it is proved that {x t } ? K converges strongly to a fixed point of T, which is also a solution of certain variational inequality. Moreover, the convergence of two explicit methods are also investigated. 相似文献
19.
Banach空间中非扩张映象的黏性逼近方法 总被引:2,自引:0,他引:2
借助Banach空间中非扩张映象的黏性逼近方法,得出了非扩张映象迭代序列收敛于其不动点的充分必要条件.本文结果推广和改进了一些人的最新结果. 相似文献
20.
A. R. Khan A. A. Domlo N. Hussain 《Numerical Functional Analysis & Optimization》2013,34(9-10):1165-1177
The aim of this paper is to obtain new coincidence and common fixed point theorems by using Lipschitz-type conditions of hybrid maps (not necessarily continuous) on a metric space. As applications, we demonstrate the existence of common fixed points from the set of best approximations. Our work sets analogues, unifies and improves various known results existing in the literature. 相似文献