共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
Under the assumption that E is a reflexive Banach space whose norm is uniformly Gêteaux differentiable and which has a weakly continuous duality mapping Jφ with gauge function φ, Ceng–Cubiotti–Yao [Strong convergence theorems for finitely many nonexpansive mappings and applications, Nonlinear Analysis 67 (2007) 1464–1473] introduced a new iterative scheme for a finite commuting family of nonexpansive mappings, and proved strong convergence theorems about this iteration. In this paper, only under the hypothesis that E is a reflexive Banach space which has a weakly continuous duality mapping Jφ with gauge function φ, and several control conditions about the iterative coefficient are removed, we present a short and simple proof of the above theorem. 相似文献
4.
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
5.
Let E be a uniformly convex Banach space which satisfies Opial’s condition or whose norm is Fréchet differentiable. Recently, Takahashi and Shimoji [W. Takahashi, K. Shimoji, Convergence theorems for nonexpansive mappings and feasibility problems, Math. Comput. Modelling 32 (2000) 1463–1471] introduced an iterative scheme given by finitely many nonexpansive mappings in E and proved weak convergence theorems which are connected with the problem of image recovery. In this paper we introduce a new iterative scheme which includes their iterative scheme as a special case. Under the assumption that E is a reflexive Banach space whose norm is uniformly Gâteaux differentiable and which has a weakly continuous duality mapping, we prove strong convergence theorems which are connected with the problem of image recovery. Using the established results, we consider the problem of finding a common fixed point of finitely many nonexpansive mappings. 相似文献
6.
Strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified Mann method. 相似文献
7.
We prove two nonlinear ergodic theorems for noncommutative semigroups of nonexpansive mappings in Banach spaces. Using these
results, we obtain some nonlinear ergodic theorems for discrete and one-parameter semigroups of nonexpansive mappings.
Dedicated to Professors Albrecht Dold and Ed Fadell 相似文献
8.
Koji Aoyama Yasunori Kimura Wataru Takahashi Masashi Toyoda 《Nonlinear Analysis: Theory, Methods & Applications》2007
In this paper, to find a common fixed point of a family of nonexpansive mappings, we introduce a Halpern type iterative sequence. Then we prove that such a sequence converges strongly to a common fixed point of nonexpansive mappings. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings and the problem of finding a zero of an accretive operator. 相似文献
9.
The main result of this paper is that a closed convex subset of a Banach space has the fixed point property for nonexpansive mappings if and only if it has the fixed point property for nonexpansive semigroups. 相似文献
10.
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
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13.
In hyperconvex metric spaces we consider best approximation, invariant approximation and best proximity pair problems for multivalued mappings that are condensing or nonexpansive. 相似文献
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15.
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
16.
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
17.
Xiaolong Qin Yeol Je Cho Jung Im Kang Shin Min Kang 《Journal of Computational and Applied Mathematics》2009
In an infinite-dimensional Hilbert space, the normal Mann’s iteration algorithm has only weak convergence, in general, even for nonexpansive mappings. In order to get a strong convergence result, we modify the normal Mann’s iterative process for an infinite family of nonexpansive mappings in the framework of Banach spaces. Our results improve and extend the recent results announced by many others. 相似文献
18.
In the present paper, we propose two kinds of new algorithms for a family of quasi-asymptotic pseudo-contractions in real Hilbert spaces. By using the proposed algorithms, we prove several strong convergence theorems for a family of quasi-asymptotic pseudo-contractions. The results of this paper are interesting extensions of those known results. 相似文献
19.
Strong convergence of an iterative method for nonexpansive mappings with new control conditions 总被引:1,自引:0,他引:1
The purpose of this paper is to study the convergence problem of an iterative method for nonexpansive mappings in Banach spaces under some new control conditions on parameters. 相似文献
20.
In this paper, we prove strong convergence theorems to a zero of monotone mapping and a fixed point of relatively weak nonexpansive mapping. Moreover, strong convergence theorems to a point which is a fixed point of relatively weak nonexpansive mapping and a solution of a certain variational problem are proved under appropriate conditions. 相似文献