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1.
The Mann iterations for nonexpansive mappings have in general only weak convergence in a Hilbert space. We modify an iterative method of Mann's type introduced by Nakajo and Takahashi [Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372–379] for nonexpansive mappings and prove strong convergence of our modified Mann's iteration processes for asymptotically nonexpansive mappings and semigroups. 相似文献
2.
Let C be a closed convex subset of a real Hilbert space H and assume that T is an asymptotically κ-strict pseudo-contraction on C with a fixed point, for some 0≤κ<1. Given an initial guess x0∈C and given also a real sequence {αn} in (0, 1), the modified Mann’s algorithm generates a sequence {xn} via the formula: xn+1=αnxn+(1−αn)Tnxn, n≥0. It is proved that if the control sequence {αn} is chosen so that κ+δ<αn<1−δ for some δ∈(0,1), then {xn} converges weakly to a fixed point of T. We also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence. 相似文献
3.
The purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of two quasi-?-nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of Banach spaces. Our results improve and extend the corresponding results announced by many others. 相似文献
4.
Vittorio Colao 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3513-3524
Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {Tn} with common fixed points, an equilibrium function G, a contraction f with coefficient 0<α<1 and a strongly positive linear bounded operator A with coefficient . Let . We define a suitable Mann type algorithm which strongly converges to the unique solution of the minimization problem , where h is a potential function for γf and C is the intersection of the equilibrium points and the common fixed points of the sequence {Tn}. 相似文献
5.
In this paper we propose a new modified Mann iteration for computing fixed points of nonexpansive mappings in a Banach space setting. This new iterative scheme combines the modified Mann iteration introduced by Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51–60] and the viscosity approximation method introduced by Moudafi [A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl. 241 (2000) 46–55]. We give certain different control conditions for the modified Mann iteration. Strong convergence in a uniformly smooth Banach space is established. 相似文献
6.
In this paper, we study boundary conditions for nonexpansive nonself-mappings in a Banach space. Using this, we prove two strong convergence theorems for nonexpansive nonself-mappings in a Banach space without boundary conditions. 相似文献
7.
8.
In this work, we give certain control conditions for a modified Ishikawa iteration to compute common fixed points of a kind of nonexpansive semigroup in Banach spaces. These results improve and extend those in Somyot and Rattanaporn (2008) [7] and Song and Xu (2008) [11]. 相似文献
9.
Shih-sen Chang H.W. Joseph Lee Chi Kin Chan 《Nonlinear Analysis: Theory, Methods & Applications》2009
In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings. The results presented in the paper extend and improve some recent results of Yao and Yao [Y.Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2) (2007) 1551–1558], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.075], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for Equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006) 506–515], Su, Shang and Qin [Y.F. Su, M.J. Shang, X.L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and Chang, Cho and Kim [S.S. Chang, Y.J. Cho, J.K. Kim, Approximation methods of solutions for equilibrium problem in Hilbert spaces, Dynam. Systems Appl. (in print)]. 相似文献
10.
Let X be a reflexive and smooth real Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation scheme xn+1=λn+1f(xn)+(1−λn+1)Tn+1xn (where f is a generalized contraction mapping) for infinitely many nonexpansive self-mappings T1,T2,T3,… in X. We establish a strong convergence result which generalizes some results in the literature. 相似文献
11.
David Ariza-Ruiz 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):1628-1640
In [5], Zamfirescu (1972) gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan, and Chatterjea. In this paper, we follow the ideas of Dugundji and Granas to extend Zamfirescu’s fixed point theorem to the class of weakly Zamfirescu maps. A continuation method for this class of maps is also given. 相似文献
12.
Summary.
In this paper we prove that the Landweber iteration is a stable
method for solving nonlinear ill-posed problems. For perturbed data with
noise level we propose a stopping rule that yields the
convergence rate
)
under appropriate conditions. We
illustrate these conditions for a few examples.
Received
February 15, 1993 / Revised version received August 2, 1994 相似文献
13.
Habtu Zegeye 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):325-329
Strong convergence theorems are obtained for a finite family of nonexpansive mappings and semigroups by the hybrid method. 相似文献
14.
A new iterative method for approximating fixed points of bounded and continuous pseudocontractive mapping is proposed and a strong convergence theorem is obtained. As an application, we prove that a slight modification of our new scheme could be employed for approximating zeros of bounded and continuous accretive operators. Our theorems extend and unify most of the results that have been proved for this class of mappings. 相似文献
15.
Let H be a real Hilbert space. Let K,F:H→H be bounded, continuous and monotone mappings. Suppose that u∗∈H is a solution to the Hammerstein equation u+KFu=0. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation. Furthermore, we give some examples to show that our result is interdisciplinary in nature, covers a large variety of areas and should be of much interest to a wide audience. 相似文献
16.
In this paper we introduce an implicit iterative scheme for finding a common element of the set of common fixed points of N nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The implicit iterative scheme is based on two well-known methods: extragradient and approximate proximal. We obtain a weak convergence theorem for three sequences generated by this implicit iterative scheme. On the basis of this theorem, we also construct an implicit iterative process for finding a common fixed point of N+1 mappings, such that one of these mappings is taken from the more general class of Lipschitz pseudocontractive mappings and the other N mappings are nonexpansive. 相似文献
17.
In this paper we propose a new modified Mann iteration for computing common fixed points of nonexpansive mappings in a Banach space. We give certain different control conditions for the modified Mann iteration. Then, we prove strong convergence theorems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These results improve and extend results of Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51–60], Yao, et al. [Y. Yao, R. Chen and J. Yao, Strong convergence and certain control conditions for modified Mann iteration, Nonlinear Anal. 68 (2008) 1687–1693], Qin and Su [X. Qin, Y. Su, Approximation of a zero point of accretive operator in Banach spaces, J. Math. Anal. Appl. 329 (2007) 415–424], and many others. 相似文献
18.
Strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified Mann method. 相似文献
19.
Hideaki Iiduka Wataru Takahashi 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3679-3688
In this paper, we study a strong convergence for monotone operators. We first introduce the hybrid type algorithm for monotone operators. Next, we obtain a strong convergence theorem (Theorem 3.3) for finding a zero point of an inverse-strongly monotone operator in a Banach space. Finally, we apply our convergence theorem to the problem of finding a minimizer of a convex function. 相似文献