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1.
In this note, we will modify several gaps in Chidume and Ofoedu [C.E. Chidume, E.U. Ofoedu, A new iteration process for generalized Lipschitz pseudo-contractive and generalized Lipschitz accretive mappings, Nonlinear Anal. (2006), in press (doi:10.1016/j.na.2006.05.012)]. 相似文献
2.
Ziming Wang Dongxing WangYucai Dong 《Journal of Computational and Applied Mathematics》2011,235(8):2364-2371
In this paper, we prove strong convergence theorems by the hybrid method for a family of hemi-relatively nonexpansive mappings in a Banach space. Our results improve and extend the corresponding results given by Qin et al. [Xiaolong Qin, Yeol Je Cho, Shin Min Kang, Haiyun Zhou, Convergence of a modified Halpern-type iteration algorithm for quasi-?-nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051-1055], and at the same time, our iteration algorithm is different from the Kimura and Takahashi algorithm, which is a modified Mann-type iteration algorithm [Yasunori Kimura, Wataru Takahashi, On a hybrid method for a family of relatively nonexpansive mappings in Banach space, J. Math. Anal. Appl. 357 (2009) 356-363]. In addition, we succeed in applying our algorithm to systems of equilibrium problems which contain a family of equilibrium problems. 相似文献
3.
Convergence of a Halpern-type iteration algorithm for a class of pseudo-contractive mappings 总被引:1,自引:0,他引:1
Let E be a real reflexive Banach space with uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed and convex subset of E. Let T:K→K be a strictly pseudo-contractive map and let L>0 denote its Lipschitz constant. Assume F(T){xK:Tx=x}≠0/ and let zF(T). Fix δ(0,1) and let δ* be such that δ*δL(0,1). Define , where δn(0,1) and limδn=0. Let {αn} be a real sequence in (0,1) which satisfies the following conditions: . For arbitrary x0,uK, define a sequence {xn}K by xn+1=αnu+(1−αn)Snxn. Then, {xn} converges strongly to a fixed point of T. 相似文献
4.
Let K be a nonempty closed convex subset of a Banach space E, T:K→K a continuous pseudo-contractive mapping. Suppose that {αn} is a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary x0∈K, the Mann type implicit iteration process {xn} given by xn=αnxn−1+(1−αn)Txn,n≥0, strongly and weakly converges to a fixed point of T, respectively. 相似文献
5.
Satit Saejung 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3431-3439
We prove strong convergence theorems for a sequence which is generated by Halpern’s iteration. We also apply our result for finding zeros of an accretive operator. Our result improves the recent result of Aoyama et al. [K. Aoyama, Y. Kimura, W. Takahashi, M. Toyoda, Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007) 2350-2360] by removing some assumptions on the parameters. Finally we discuss the new sufficient condition studied by Song [Y. Song, A new sufficient condition for the strong convergence of Halpern type iterations. Appl. Math. Comput. 198 (2) (2008) 721-728; Y. Song, New strong convergence theorems for nonexpansive nonself-mappings without boundary conditions. Comput. Math. Appl. 56 (6) (2008) 1473-1478] and correct the main result of Song and Chai [Y. Song, X. Chai, Halpern iteration for firmly type nonexpansive mappings, Nonlinear Anal. 71 (10) (2009) 4500-4506]. 相似文献
6.
We study the strong convergence of two viscosity iteration processes for pseudo-contractive semigroup and for ?-strongly pseudo-contractive mapping in uniformly convex Banach spaces with uniformly Gâteaux differentiable norm. As special cases, we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain Banach spaces. The results presented in this paper extend and generalize previous results. 相似文献
7.
Habtu Zegeye Naseer Shahzad Mohammad A. Alghamdi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7304-7311
Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→C,i=1,2,…,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa’s method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set Cn for each n≥1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings. 相似文献
8.
A new iteration process is introduced and proved to converge strongly to a common fixed point for a finite family of generalized Lipschitz nonlinear mappings in a real reflexive Banach space E with a uniformly Gâteaux differentiable norm if at least one member of the family is pseudo-contractive. It is also proved that a slight modification of the process converges to a common zero for a finite family of generalized Lipschitz accretive operators defined on E. Results for nonexpansive families are obtained as easy corollaries. Finally, the new iteration process and the method of proof are of independent interest. 相似文献
9.
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
10.
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
11.
In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding results of many others. 相似文献
12.
Shahram Saeidi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):546-548
In this note, we deal with an iterative scheme of Halpern type for a semigroup of nonexpansive mappings on a compact convex subset of a strictly convex and smooth Banach space with respect to an asymptotically left invariant sequence of means defined on an appropriate space of bounded real valued functions of the semigroup. We improve the corresponding result of [A.T. Lau, H. Miyake, W. Takahashi, Approximation of fixed points for amenable semigroups of nonexpansive mappings in Banach spaces, Nonlinear Anal. 67 (2007) 1211-1225]. 相似文献
13.
The purpose of this paper is to study the strong convergence of a process of implicit iteration to a common fixed point for a finite family of asymptotically hemi-contractive mappings. Our results extend a recent result of M.O. Osilike and B.G. Akuchu [Common fixed points of a finite family of asymptotically pseudocontractive maps, Fixed Point Theory Appl. 2 (2004) 81–88] from Hilbert spaces to p-uniformly convex Banach spaces with p>1. 相似文献
14.
In this paper we propose a new implicit iteration scheme with perturbed mapping for approximation of common fixed points of a finite family of nonexpansive mappings. We establish some convergence theorems for this implicit iteration scheme. In particular, necessary and sufficient conditions for strong convergence of this implicit iteration scheme were obtained. 相似文献
15.
Ali Abkar Mohammad Eslamian 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):1895-1903
We establish △-convergence and strong convergence theorems for an iterative process for a finite family of generalized nonexpansive multivalued mappings in a CAT(0) space. Moreover, we present a fixed point theorem for a pair consisting of a finite family of generalized nonexpansive single valued mappings, and a generalized nonexpansive multivalued mapping in CAT(0) spaces. 相似文献
16.
Ci-Shui Ge 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(5):2859-2866
The purpose of this article is to propose a new hybrid algorithm with variable coefficients and prove convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense on unbounded domains. The results of the paper improve and extend the recent results of Qin et al. [X.L. Qin, S.Y. Cho, J.K. Kim, Convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense, Fixed Point Theory Appl. 2010, doi:10.1155/2010/186874, Article ID 186874, 14 pages] and several others. The algorithm with variable coefficients introduced in this paper is of independent interest. 相似文献
17.
Convergence and certain control conditions for hybrid viscosity approximation methods 总被引:1,自引:0,他引:1
Very recently, Yao, Chen and Yao [20] proposed a hybrid viscosity approximation method, which combines the viscosity approximation method and the Mann iteration method. Under the convergence of one parameter sequence to zero, they derived a strong convergence theorem in a uniformly smooth Banach space. In this paper, under the convergence of no parameter sequence to zero, we prove the strong convergence of the sequence generated by their method to a fixed point of a nonexpansive mapping, which solves a variational inequality. An appropriate example such that all conditions of this result are satisfied and their condition βn→0 is not satisfied is provided. Furthermore, we also give a weak convergence theorem for their method involving a nonexpansive mapping in a Hilbert space. 相似文献
18.
Convergence of an implicit iterative process for asymptotically pseudocontractive nonself-mappings 总被引:1,自引:0,他引:1
Xiaolong Qin Sun Young Cho 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):5851-5862
In this work, an implicit iterative process is considered for asymptotically pseudocontractive nonself-mappings. Weak and strong convergence theorems for common fixed points of a family of asymptotically pseudocontractive nonself-mappings are established in the framework of Hilbert spaces. 相似文献
19.
We study approximation of common fixed points of a finite family of nonexpansive mappings and introduce an iterative scheme defined by using a convex combination of mappings. Strong convergence of the iteration is obtained under several types of control conditions.Received: 28 May 2004 相似文献
20.
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