weak and strong convergence in hilbert spaces

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Ngày tải lên: 23/06/2014, 00:20

... 11 10. Xu, HK: Inequalities in Banach spaces with applications. Nonlinear Anal. 16, 1127–1138 (1991). doi:10.1016/0362-546X(91) 90200-K 11. Schu, J: Weak and strong convergence to fixed points of asymptotically ... strong convergence theorem of an implicit-shrinking iterative process for two nonexpansive mappings and a relative nonexpansive mapping on Banach spaces. Note that the conditions of strong convergence ... different from the strong convergence theorems for the implicit iterative processes in the literatures. Finally, we discuss a strong convergence theorem concerning two nonexpansive mappings and the resolvent...

Ngày tải lên: 20/06/2014, 21:20

... quasinonexpansive mapping. However, the converse may be false [1, Example 2]. Construction of approximating fixed points of nonlinear mappings is an important subject in the theory of nonlinear mappings and its ... c n = Lin et al. Fixed Point Theory and Applications 2011, 2011:96 http://www.fixedpointtheoryandapplications.com/content/2011/1/96 Page 14 of 20 12. James, RC: Inner products in normed linear spaces. ... Banach space and let E* b e the dual space of E. For a sequence {x n }ofE and a point x Î E, the weak convergence of {x n }tox and the strong convergence of {x n }tox are denoted by x n ⇀ x and x n ®...

Ngày tải lên: 20/06/2014, 21:20

... 3502–3511, 2009. 8 M. O. Osilike and S. C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings,” Mathematical and Computer Modelling, vol. 32, no. 10, ... Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, ” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 336–346, 2007. Fixed Point ... κ-strict pseudocontractions was introduced by Qihou 4 in 1996 see also 5.KimandXu6 studied weak and strong convergence theorems for this class of mappings. It is important to note that...

Ngày tải lên: 21/06/2014, 11:20

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... North-Holland, Amsterdam, The Netherlands, 2001. 11 H. Iiduka and W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse- strongly monotone mappings,” Nonlinear Analysis: ... and Strict Pseudocontractions in Hilbert Spaces Ming Tian College of Science, Civil Aviation University of China, Tianjin 300300, China Correspondence should be addressed to Ming Tian, tianming1963@126.com Received ... pseudocontraction mapping in the setting of real Hilbert spaces. We proved strong convergence theorems of the sequence generated by our proposed schemes. 1. Introduction Let H be a real Hilbert space and C a...

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... Combettes and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces, ” Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005. 24 W. Takahashi, Weak and strong convergence ... Method for In nite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces Shenghua Wang 1, 2 and Baohua Guo 1, 2 1 National Engineering Laboratory ... Wang, G. Marino, and F. H. Wang, Strong convergence theorems for a generalized equilibrium problem with a relaxed monotone mapping and a countable family of nonexpansive mappings in a hilbert space,”...

Ngày tải lên: 21/06/2014, 11:20

... Pseudocontractive Mappings in Hilbert Spaces Xiaolong Qin, 1 Sun Young Cho, 2 and Shin Min Kang 3 1 School of Mathematics and Information Sciences, North China University of Water Resources and Electric ... mappings. A weak convergence theorem of fixed points is established in the framework of Hilbert spaces. 1. Introduction and Preliminaries Throughout this paper, we always assume that H is a real Hilbert ... pseudocontractions was introduced by Browder and Petryshyn 11 in a real Hilbert space. In 2007, Marino and Xu 12 obtained a weak convergence theorem for the class of strictly pseudocontractive mappings; see...

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... nonexpansive mappings in Hilbert spaces. 2010 International Conference on Computational Intelligence and Software Engineering, CiSE 2010 (2010). art. no. 5677064 7. Maingé, PE: Strong convergence ... Access Strong convergent result for quasi-nonexpansive mappings in Hilbert spaces Ming Tian * and Xin Jin * Correspondence: tianming1963@126.com College of Science, Civil Aviation University of China, ... nonexpan- sive mapping T. In 2009, Maingè [4] considered the viscosity approximation method (1.1), and expanded the strong convergence to quasi-nonexpansive mappings in Hilbert space. In 2010, Tian...

Ngày tải lên: 20/06/2014, 22:20

... as: Wang and Wang: On relaxed and contraction-proximal point algorithms in hilbert spaces. Journal of Inequalities and Applications 2011 2011:41. Submit your manuscript to a journal and benefi ... University, Luoyang 471022, China Abstract We consider the relaxed and contraction-proximal point algorithms in Hilbert spaces. Some conditions on the parameters for gu aranteeing the convergence of the algorithm ... ∞ , where ˜ x n = J c n (x n + e n ) . In 2001, Han and He [2] proved that in finite dimensional Hilbert space criterion (II) can be replaced by Wang and Wang Journal of Inequalities and Applications 2011, 2011:41 http://www.journalofinequalitiesandapplications.com/content/2011/1/41 ©...

Ngày tải lên: 21/06/2014, 00:20

... and reproduction in any medium, provided the original work is properly cited. monotone mapping, T: K ® Hbel-inverse strongly monotone mapping. If g is an expanding affine continuous mapping and ... I - F is an inverse strongly mono- tone mapping, and the fixed points set of mapping F and the solution set S(I - F)are equal. This means that our results contain the study of finding a common ... results and definitions. Definition2.1.LetA: H ® H be a mapping and K ⊂ H.Then,A is said to be semi- continuous at a point x in K if lim t → 0 A(x + th), y = A(x), y, x + th ∈ K, y ∈ H . Definition2.2....

Ngày tải lên: 21/06/2014, 01:20

... pages doi:10.1155/2010/547828 Research Article Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces Yuan Qing, 1 Xiaolong Qin, 1 Haiyun Zhou, 2 and Shin Min Kang 3 1 Department of Mathematics, ... RA to denote the domain and the range of the mapping A. → and  denote strong and weak convergence, respectively. Recall the following well-known definitions. 1 A mapping A : C → H is said ... T is said to be hemicontinuous if it is continuous from each line segment in X to the weak topology in X ∗ . 7 The mapping f with the domain Df and the range Rf in H is said to be pseudocontractive...

Ngày tải lên: 21/06/2014, 07:20

... 1.2 converges weakly to a point in FT. Therefore, many authors try to modify Mann’s iteration process to have strong convergence. In 2005, Kim and Xu 3 introduced the following iteration ... mapping K n is called the K-mapping generated by T 1 , ,T N and γ n,1 ,γ n,2 , ,γ n,N . In this paper, motivated by Kim and Xu 3,MarinoandXu10,Xu5, Yao et al. 4, andShang et al. 8, we introduce ... original work is properly cited. We introduce a new general iterative method by using the K-mapping for finding a common fixed point of a finite family of nonexpansive mappings in the framework of Hilbert...

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