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1.
In this paper, we consider the weak and strong convergence of an implicit iterative process with errors for two finite families of asymptotically nonexpansive mappings in the framework of Banach spaces. Our results presented in this paper improve and extend the recent ones announced by many others.  相似文献
2.
The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variation inequalities for a relaxed cocoercive mapping and the set of solutions of an equilibrium problem. Our results extend recent results announced by many others.  相似文献
3.
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: KE 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 = {xK: 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 nN and some > 0. Starting from arbitrary x 1K 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 pF; (ii) If T satisfies condition (A′) then {x n } converges strongly to a common fixed point pF.   相似文献
4.
In this paper, we study minimal zero norm solutions of the linear complementarity problems, defined as the solutions with smallest cardinality. Minimal zero norm solutions are often desired in some real applications such as bimatrix game and portfolio selection. We first show the uniqueness of the minimal zero norm solution for Z-matrix linear complementarity problems. To find minimal zero norm solutions is equivalent to solve a difficult zero norm minimization problem with linear complementarity constraints. We then propose a p norm regularized minimization model with p in the open interval from zero to one, and show that it can approximate minimal zero norm solutions very well by sequentially decreasing the regularization parameter. We establish a threshold lower bound for any nonzero entry in its local minimizers, that can be used to identify zero entries precisely in computed solutions. We also consider the choice of regularization parameter to get desired sparsity. Based on the theoretical results, we design a sequential smoothing gradient method to solve the model. Numerical results demonstrate that the sequential smoothing gradient method can effectively solve the regularized model and get minimal zero norm solutions of linear complementarity problems.  相似文献
5.
In this paper, we introduce a multiple-step iterative process for approximating a fixed point of nonexpansive mappings in the framework of uniformly smooth Banach spaces and reflexive Banach spaces which have a weakly continuous duality map, respectively. The results presented in this paper improve and extend the corresponding results of announced by many others.  相似文献
6.
Let K be a nonempty closed convex subset of a real Hilbert space H such that K ± KK, T: KH a k-strict pseudo-contraction for some 0 ⩽ k < 1 such that F(T) = {xK: x = Tx} ≠ $ \not 0 $ \not 0 . Consider the following iterative algorithm given by
$ \forall x_1 \in K,x_{n + 1} = \alpha _n \gamma f(x_n ) + \beta _n x_n + ((1 - \beta _n )I - \alpha _n A)P_K Sx_{n,} n \geqslant 1, $ \forall x_1 \in K,x_{n + 1} = \alpha _n \gamma f(x_n ) + \beta _n x_n + ((1 - \beta _n )I - \alpha _n A)P_K Sx_{n,} n \geqslant 1,   相似文献
7.
In this paper, we modify the normal Mann’s iterative process to have strong convergence for a kk-strictly pseudo-contractive non-self mapping in the framework of Hilbert spaces. Our results improve and extend the corresponding results announced by many others.  相似文献
8.
In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Our results improve and extend the recent ones announced by Chen et al. [J.M. Chen, L.J. Zhang, T.G. Fan, Viscosity approximation methods for nonexpansive mappings and monotone mappings, doi:10.1016/j.jmaa.2006.12.088], Iiduka and Tahakshi [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350], Yao and Yao [Y.H. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput, doi:10.1016/j.amc.2006.08.062] and Many others.  相似文献
9.
In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extended and improved the results of H. Iiduka and W. Takahashi [Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350] and S. Takahashi and W. Takahashi [Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515]. Therefore, by using the above result, an iterative algorithm for the solution of a optimization problem was obtained.  相似文献
10.
The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of variational inequality for a relaxed cocoercive mapping and the set of solutions of an equilibrium problem. Our results extend the recent results of Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515], Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43–52], Combettes and Hirstoaga [P.L. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 486–491], Iiduka and Takahashi, [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350] and many others.  相似文献
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